You need to distinguish their opinion of the Spanish prior to the defeat of the Aztecs and after. When the Spanish first arrived, they had guns and horses but were small in number. The native americans had yet to suffer the full depravities of not only the Spanish but also the deadly diseases to come, and they were strong both in population numbers and in military prowess; they considered themselves allied to Cortes, not under his rule. That was certainly a better position than being under the Aztecs' heels. I suspect your quote comes from this period.
Indeed, it took Cortes a fair bit of campaigning (and a major near defeat) to secure military victory over the Aztecs. It helped that he had help in the form of reinforcements, indian allies, and smallpox. Eventually he defeated the Aztecs, banished them from Tenochtitlan, destroyed the temples, and rebuilt it into Mexico City.
With Mexico City as their base, the Spanish essentially just inserted themselves into the power structure the Aztecs had created and occupied. This worked because the "Aztec empire" was not a unified empire in the sense of say the Roman empire, but was more like a loose feudal collection of city states that cooperated out of fear of retribution; the Aztecs weren't "rulers" of these polities any more than the Chicago mafia were "employers" of the shopkeepers they shook down or the police they bribed. So, the Spanish conquistadors could simply break a few legs and become the new boss, same as the old boss. In fact even after Cortes, fighting ("pacification") continued for 60 years.
The Spanish colonists recognized the indigenous nobility, with privileges, education, and even titles. So in a lot of places, the powers that had been, continued to be, and life went on as before. Even the infamous Spanish slavery was essentially a continuation of long established forced labor practices, just taken up a few notches. This was justified with the belief that the Spanish were providing protection and Christian education to the natives.
As well, we should probably distinguish between the different groups of Native Americans, they weren't all the same. We can imagine that groups that fought WITH the Spanish were treated better than ones that fought against them. But regardless, all bets were off if silver mines were discovered near you; the Spanish tapped tribes pretty intently to work their mines.
So, did some Native Americans prefer Spanish rulers to the Aztecs? If you were in the nobility, had supported Cortes in battle, and didn't have any silver deposits near you, the Spanish probably weren't too bad. Maybe you'd get to learn to read.
For a lot of Native Americans, though, life under the Spanish was not much different than under the Aztecs. A lot less human sacrifice, a lot more forced labor, and plenty of smallpox.