In interested circles of archaeology the discovery of Gilgamesh epos was a sensation as well. Old writings 'from the time of biblical history'. And obviously originals, not copies of copies. Deciphering and translating them was a great show of scientific progress and greatly increased the popularity of the study and translation of cuneiform texts.
But the first versions of Gilgamesh did not contain 'the flood part'.
When that part was found on the famous flood tablet K.3375 it excited the public's mind. Mainly because the publication George Smith put forward had a very catchy title that epitomized the teleological goal of most archaeology of a certain subfield: to use science 'to prove the bible was right'. This was biblical archaeology.
The tablet not only talks of a great flood, it does so in the alleged biblical homeland of some of the protagonists from the first book of Mose. And it does so in striking parallel down to some of the verses used.
Utnapishtim’s story of the flood takes up almost two hundred lines of Tablet 11. The account of the flood shares so many details with the later biblical account that it is not surprising that this section of Gilgamesh created a sensation in the 1870s when George Smith found the tablets at Nineveh. Some lines are so close to the Bible that they provide the best parallel to biblical texts among the many cuneiform texts that have been discovered since then. The very prominence of the flood story in Tablet 11 creates a problem for a unified reading of Gilgamesh.
When George Smith—the Englishman who found the most important Gilgamesh tablets in the ancient Assyrian city of Nineveh—came across the lines that described the great Flood, a witness reported that Smith was so excited that he started pulling off his clothes. In the hallowed British Museum, of all places. And Smith subsequently published his translation of Gilgamesh with a title that tells us what made the ancient story a sensation in his time: The Chaldean Account of Genesis (1875). By “Chaldean” Smith meant Mesopotamia generally, at least the southern part from Babylon down to the Arabian (or Persian) Gulf. The reference to “Genesis” would have been even clearer to his readers in the 1870s than it is today, the first book of the Bible, which, of course, contains the biblical story of the Flood (Genesis 6-9). Smith devoted six chapters of The Chaldean Account of Genesis to the story of Gilgamesh. But he saw, or thought he saw, from the Flood story in Gilgamesh that the heroic tale was itself only a part of a large literature in Mesopotamia that described Creation, the Tower of Babel, the destruction of Sodom and the times of the Patriarchs.
— John R. Maier: "Gilgamesh and the Great Goddess of Uruk", SUNY Brockport eBooks, 4, 2018.
Today one may interpret this not really as 'see, they saw it too and wrote about, so it must be factually true'. The more down to earth interpretation is 'see, the older text is likely the inspiration for a later copy of this theme we now still find in every bible printed, what an ancient tradition of an interesting story well told'.
And this more modern interpretation is also the actual effect on most critical scholars since then. A perhaps also noteworthy feat was Smith's public relations effort:
In the 1820s, Old Testament interpreters were challenged by the findings of geologists, who argued that the world was thousands (sic) of years older than was implied by the Old Testament figures. (According to Archbishop Ussher's very influential interpretation of these figures the world had been created in 4004 BCE.) The response of orthodox interpreters to the geologists was that the Flood had destroyed and distorted the original layers of the earth. The geologists were therefore being misled by their findings. The next challenge came from the publication of Darwin's Origin of Species in 1859. This was a challenge to Genesis 2-3, for if it was true that humankind had gradually evolved from elementary life forms, what was one to make of the biblical story that a once perfect human couple had 'fallen'?
The most interesting challenge to the interpretation of Genesis 1-11, however— and the one that will concern us here—came towards the end of the nineteenth century with the discovery of ancient Babylonian texts that contained material similar to that in Genesis 1-11. On 3 December 1872 a young scholar on the staffof the British Museum, George Smith, gave a lecture entitled The Chaldean Accountof the Deluge'. It dealt with what is now known to be part of Tablet XI of the Epic of Gilgamesh. In 1875 Smith announced, in a letter to a London newspaper, the discovery of a Babylonian account of creation, part of the text now known as Enuma Elish. These discoveries aroused a great deal of interest, and within a few years Old Testament scholars began to argue that the material in Genesis was in fact depend- ent upon Babylonian material.
— John Rogerson & Philip R. Davies: "The Old Testament World", T&T Clark International: London, New York, 22007.
Then the discoverer himself, his personality and biography made for an excellent story:
As scholars go, Smith, 32 years old, was an anomaly; he had ended his formal education at age 14 when he was apprenticed to a printer, and perhaps it was because of his training as an engraver that he had such a knack for assembling coherent passages of cuneiform out of the drawers and drawers of old rubble. In fact, Smith had already established dates for a couple of minor events in Israelite history, and on this brisk fall day he was looking for other references that might confirm parts of the Bible. […]
Eager to become a full-fledged archaeologist, Smith longed to go to Iraq to excavate. But museum trustees felt that they had more than enough Assyrian and Babylonian artifacts and wanted Smith at work on the premises. He had no way to support himself in a distant province of the Ottoman Empire, or even to pay his own way there, as he was now supporting a wife and a growing family on his slender wages. Discouraged, he wrote to a friend in February 1872 that the "Government will not assist the movement in the least, at present, in fact I think they will not give a penny until something is discovered." It was then that Smith began systematically surveying the museum's collection for texts that might shed new light on biblical studies. In chancing upon the Flood story, Smith felt he had found the passport to the land of his dreams.
Word of the find spread rapidly, and Prime Minister Gladstone himself was in the audience when Smith presented a lecture to the Biblical Archaeology Society on December 3, 1872. Edwin Arnold, editor of the Daily Telegraph, promptly put up the sum of a thousand guineas to fund Smith on an expedition—much as the Telegraph had successfully sent Henry Morton Stanley to find the explorer-missionary David Livingstone in Central Africa, after Livingstone had ceased to be in contact with England during a long journey of exploration begun in 1866. In January 1873, Smith was at last on his way.[…]
Back in London, Smith found himself famous. The Daily Telegraph had run articles trumpeting
"THE DAILY TELEGRAPH"
COMPLETE SUCCESS OF EXCAVATIONS
THE MISSING PORTION OF THE DELUGE
— David Damrosch: "Epic Hero. How a self-taught British genius rediscovered the Mesopotamian saga of Gilgamesh after 2,500 years", Smithsonian Magazine, May 2007.
sermons and newspaper editorials began to engage in sharp debate: What did the Babylonian version prove, the truth of biblical history or its falsity? As the New York Times noted in a front-page article,
“For the present the orthodox people are in great delight, and are very much prepossessed by the corroboration which it affords to Biblical history. It is possible, however, as has been pointed out, that the Chaldean inscription, if genuine, may be regarded as a confirmation of the statement that there are various traditions of the deluge apart from the Biblical one, which is perhaps legendary like the rest.”
Smith’s scholarly detective work brought the ancient epic squarely into the middle of the heated Victorian controversy over creation and evolution, religion and science, a debate that continues today.
— David Damrosch: "The Buried Book: The Loss and Rediscovery of the Great Epic of Gilgamesh", Henry Holt: New York, 2006.
Update for the edited question and the subquestion contrasting other floods:
Ancient Greek flood myths are content-wise 'a flood', sharing the topos or theme, but not the details with the Noah-story, except for the Deucalion version, but even versions of that diverge more from either Noah or Gilgamesh.
They did not survive as well in material form as tablets or scrolls, not unlike the biblical stories, but unlike Gilgamesh.
While Greek versions 'are set' in 'primordial times', the surviving copies of for example the deluge accounts of Deucalion are in Ovid and Pseudo-Apollodorus or the Parian Chronicle (on that stone of course just in allusional shortened form).
It was easy to argue that the book of Genesis was written early (or even for some by Mose himself, who 'lived' much earlier than those Greek and Roman sources), arriving at the claim that the later sources are dependent on the Hebrew story, a distortion through copying, from another cultural realm / part of the ancient world etc.
It is quite difficult to argue all of that for Gilgamesh or Atra-Hasis. A record set in 'stone' with a lot of shared material for which biblical 'originals' (as in: oldest material form with text, manuscripts) were more than thousand years younger (at the time).
Most important here is the observation that the language and style used is so similar, that the bible sticks out as not formulated very originally. For example: The whole Old Testament uses the word for pitch for the ark (Gen 6,14) בַּכֹּֽפֶר kopær only once ever (16 occurences of the same letter sequence but with a whole different meaning, same meaning found usually in חֵמָר chemar). However, Akkadian 𒇒𒌓𒀀 kupru is a close match as a loanword and in all versions of ancient Orient flood myths.
This is one of the arguments that 'really, everything was invented' 'in Mesopotamia' (in the extreme even including Judaism and the bible): Panbabylonism, a 'school of thought' or perhaps 'ideology' just developing at the time. In an almost parallel development the new documentary hypothesis for 'dating the bible' must be considered, making the biblical text as a whole appear as of much younger origin than previously thought. Especially those texts that date from post-exilic times, which include some parts of the Priestly source as used interwoven in the relevant part of Genesis, were then seen as 'obviously much younger than any Babylonian version…'
In contrast to this Smith described his finds as:
A short time back I discovered among the Assyrian tablets in the British Museum, an account of the flood […]
these copies belong to the time of Assurbanipal, or about 660 years before the Christian era, and they were found in the library of that monarch in the palace at Nineveh. The original text, according to the statements on the tablets, must have belonged to the city of Erech [Uruk], and it appears to have been either written in, or translated into the Semitic Babylonian, at a very early period.
— Michael Schmidt: "Gilgamesh. The Life of a Poem", Princeton University Press: Princeton, Oxford, 2019.
A great overview and comparison of Babylonian, Hebrew and Greek flood myths is found here:
The myth of the Great Flood was not among the most popular stories in Greece and Rome. We find hardly any pictures of Deucalion and Pyrrha, the two heroes of the western version of the myth. One reason is that the Greeks were not afraid of water in a way comparable to the Babylonians. Their rivers, the Euphrates and Tigris, flooded when the wheat and barley were ripe: at the wrong moment. A river flood was a catastrophe indeed. Greek agriculture, on the other hand, depended on rainfall, and the Greeks hardly knew what a river flood meant.
The oldest reference to the Great Flood in Greek literature can be found in the works of Epicharmus, a comic poet from Sicily whose activity can be dated to the first quarter of the fifth century BCE.Comicorum Graecorum Fragmenta in Papyris Reperta 85, fr.1. Just as old is Olympic Ode 9 by Pindar. It is possible that Hesiod also referred to the Flood, because in a fragment from his Catalog of Women, he refers to Deucalion. If the Catalog is authentic, which we do not know for certain, the myth of the Flood was current in Greece before c.600 BCE.
In the second century BCE, the story was briefly retold in The Library, a work attributed to Apollodorus of Alexandria (text), and in the first century CE, the Roman author Hyginus did the same in a couple of lines (text). The longest version, however, was written by the Roman poet Ovid (text).
— "The Great Flood: Graeco-Roman version", Livius.org, 2017; last modified on 14 April 2020.