In his letter to Charles V, Hernan Cortes states that "it was only necessary to threaten to return them [the natives] to their native masters in order to make them serve the Spaniards very willingly." (source: "The Encomienda in New Spain: The Beginning of Spanish Mexico", pp. 61).
Is there evidence (other than Cortes' own view, which is obviously biased) to suggest that some Native Americans did in fact prefer Spanish rulers?
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.
Two words: "Human Sacrifice":
Because the objective of Aztec warfare was to capture victims alive for human sacrifice, battle tactics were designed primarily to injure the enemy rather than kill him. After towns were conquered their inhabitants were no longer candidates for human sacrifice, only liable to regular tribute. Slaves also could be used for human sacrifice, but only if the slave was considered lazy and had been resold three times.
Aztecs did that, Spanish did not.
PS. No, the Spanish were no fluffy little bunnies handing out sweets. However, in general, they did not kill for no good reason those who served them, unlike the Aztecs.
I think a bit of context might help. The natives Cortes is talking about had been subject tribes of the Aztecs who took the opprotunity to rise against them and to ally themselves with the Spanish.
What Cortes was doing, then, was browbeating his allies into submission by the threat of turning them over to their erstwhile masters. A somewhat underhanded technique, of course.
This has nothing to do, as far as I can tell, with the comparative advantages of Spanish or Aztec rule, just a bit of power play on Cortes's part.
There was one group of Native Americans in Mexico, the Tlaxcala, who allied with the Spanish against the "Aztec" cities of Tenochtitlan, Texcoco, and Tlacopan. The Tlaxcala formed the backbone (other than the Spanish) of the anti-Aztec coalition.
When Cortes was in retreat, the Aztecs asked the Tlaxcalans to "turn over" Cortes to them. One of the younger chiefs agreed, but he was vetoed (and later killed) by his elders.
After they defeated the Aztecs together, the Tlaxcalans were allowed by the Spanish to participate in the conquest of Guatemala, and were generally treated by them as "favored" Native Americans compared to the defeated Aztecs. But the losses they suffered supporting the Spanish (and from diseases, etc.) caused them to die out.
For the Tlaxcalans, at least, "the enemy of my enemy is my friend."
