If it's on topic, I'm also interested to know how they compare against modern steel.
Toledo steel was a very good steel, comparable to mainstream contemporary ones. It is based mostly on the content of the material and way of hardening. Now the best European steel for blades is not Spanish, but Swedish V10.
With Damascus there is a wide-spread fallacy. What is now called "true damascus" - blades based on the way of smithing of two or more steels - folding, beating, folding again,.. 32 or 256 or even thousands of layers... It has very nice looking, and can be very good (depending on the source steels and regime of hardening), but it is NOT the true damascus.
As for the last, now it is called wootz. The inner structure of wootz was created by not mechanical process, but by special regimes of hardening, when crystals of different steels are growing inside the ingot and filling it with the inner structure. Of course, composition of the steel is extremely important, too. The last can be repeated, but the secret of hardening is lost. Now you can buy only OLD blades or ingots of wootz made of OLD blades. What is the sense of the last, I don't know. But they are not expensive, in contrary to the old blades.
There existed close variants - reinventions in other countries, Russian bulat was one of them, according to legends. The Damascus steel could be extremely sharp and simultaneously, very strong - you could cut a silk scarf by letting it to fall on the blade and you could use the same blade as a belt and you could simply cut a usual sword in two.
As for samurai weapon, it is a widespread mistake, that it had good steel. On the contrary, the steel was brittle, in Japanese fencing you should never block the blow, but let it slip along the blade. Though this steel could be sharpen also to the extreme, and the trick with a scarf could be done with it, but it was weak and easily broken or at least dented by any direct blow. The Japanese did the most possible out of what they had, but the resources on the Japan islands are poor.
On the other side, now, while Japan masters can reach the all Mendeleev table from all the World, the best steel is made by them - blue and white steel (non-stainless ones)and the star of all - ZDP-189, with hardness 63 (other blades reach 60 at best) and stainless, too, with unknown receipt.
Japanese now make saws with hardness of 73!, which can be sharpened by diamond only, but this steel is not plastic enough to be a cold weapon steel.
An interesting professional article on the theme, much more thorough than my answer: http://www.tf.uni-kiel.de/matwis/amat/def_en/articles/vikingsword/blade_patterns_intrinsic.html
The problem is that now all these names are mixed - you can buy a "japanese damascene" for 100 dollars. Not real, of course. http://www.swordsoftheeast.com/damascus_3.aspx.
The secret of toledo swords is revealed now: http://aceros-de-hispania.com/toledo-swords.htm
An interesting personal research with links: http://tf.uni-kiel.de/matwis/amat/def_en/index.html
As it is, all three are interesting for being completely different methods of achieving a high quality of steel. Equally interesting is that they are each of high quality in different ways.
As for Tamahagane, the iron that was available in Japan was actually very poor compared to that found in Europe. It had a characteristically low carbon content, and the only way they had to increase the carbon content was to fold it into the steel during forging with a process called pattern welding. This folding did make the steel harder, and thus better able to hold an edge and less likely to bend, but it also meant that it was more brittle and more likely to chip and crack as well.
Damascus steel is something of an oddity when discussing forging technology for two reasons. Firstly, historians don't know if the descriptor refers to the smiths working the steel, where it was sold, or simply a visual similarity to textiles from the Byzantine empire. Secondly, the exact methods originally used to forge the steel in question have been lost to time. Researchers have found the various trace elements within the metal, but they don't know precisely how they were introduced. At its core, however, Damascus steel is basically another type of pattern weld. The problems this introduces are the same that are introduced with modern welding techniques, in that each weld represents a point where two pieces of metal are joined and are thus weaker than a solid piece of the same material would be.
Toledo steel, however, is separated from the other two in that it is a true alloy. Toledo steel is created by permanently mixing the iron and the other chemical additives through smelting. The difference is visibly evident by the observing the consistent appearance of Toledo steel versus the layered patterns of both Tamahagane and Damascus steel. Of course, like the other types of steel, Toledo had its drawbacks. Because of the extremely tight tolerances of the heat used during the smelting, forging, and tempering processes, the steel took an incredibly long time to create. This lead to the widespread use of daggers and shortswords, as they required less material and thus less time to create than a full-sized sword.
As for determining which of them was the best, that is completely subjective, depending on the desired characteristics, much like deciding which is better between a wrench and a hammer. A wrench is good for turning bolts, but a hammer is good for driving nails. Similarly, it can't really be said which method of producing steel is better without defining the criteria. Tamahagane could be honed to an incredibly sharp edge, but was too brittle to be used for blocking. This was fine, as most combat with katanas and similar weapons was against combatants in leather or lacquered bamboo armor. I'm not sure of the hardness characteristics of Damascus steel or the type of armor that it would have been used against, but due to the similarities it has with tamahagane, I imagine it faced similar challenges as well. Toledo steel, being produced in western Europe, would have often been used against more heavily armored opponents or against shields. For this reason, it would have been less important that the steel be able to hold a perfect edge than the tendency not to break when impacting something it couldn't cut straight through.
So, to answer the original question of a comparison between the three kinds of steel, I doubt that you would be able to find anything that addressed it without doing so in the context of making blades, as steel that was used for other purposes was typically of a different formulation. And, to answer the second question, contemporary formulas have been invented which surpass all three in just about any category you could think of. After all, there have been thousands of years of technological advances since the invention of these methods, depending on which you are referring to.
A portion of one of the ancient Damascus steel blades was removed and examined, the molecular structure was made up of a series of carbon nanotubes around iron nanowires. It's unknown as to how this was achieved, and hasn't been replicated by modern humans. It's sometimes referred to as Wootz steel. Ref
Modern attempts at replicating Damascus steel involves stacking alternating sheets of high carbon and medium carbon into a bar, heating the bar and twisting the bar over, before folding it back on itself and hammering flat again. This could be repeated several times, less than 10 I would presume. Too many folds will begin to undo the work. like a croissant
As far as I know, the Japanese folded steel is exaggerated. the "pig iron" that was available would need to be strengthened by hammering to remove slag impurities, and thus would become folded over itself several times, but it was still only "wrought iron" at that point, and was still inferior to "crucible steel" which was only discovered in the 17 century by the Europeans, but had been used in Asia much earlier. From the 8th century, the vikings may have learned the crucible steel techniques from the middle east, but 'forgot' them by some time around the 11th century. Look up the "Ulfberht" swords.
Something I learned recently was that the Katana's strength came from it's use of wrought iron as a body for the sword, with an edge made of high carbon steel to allow it to have strength while cutting, but maintain flexibility and avoid snapping.
So long story short, ancient Damascus steel exceeds modern steel hypothetically.
Japanese steel was not particularly advanced, so unfortunately it would be very much outperformed by modern steel. The superior engineering of the sword structure was the Katana's great strength.
And I do not know about Toledo steel, so I'll have to do some research