The early encomenderos wanted their encomiendas to be essentially feudal fiefs- that is what power and prestige looked like in their homeland. Legally, the encomiendas were not feudal in nature, but in practice they were often even more exploitive.

First of all, an encomienda is a grant of people (or souls), not land as in feudalism (even though that land might come with the serfs on it). Ostensibly, the encomienda represented a responsibility to look after the spiritual welfare of the souls under their care, and in return for doing this 'selfless' Christian act, they could require labor from their indios. Of course, although the indios were often subjected to mass baptisms, very little actual instruction in the Catholic faith occurred. Instead, with few checks on their authority, the encomenderos exploited as much labor (or tribute) out of their subjects as possible. They were not legally serfs or slaves, but were treated no better than if they had been.

Bartolomé de las Casas, a former encomendero turned Dominican friar, was the most influential advocate for the rights of the indigenous peoples. He had witnessed firsthand how forced labor had depopulated Hispaniola and sought an abolition to the encomienda system. Las Casas got what he wanted in the form of the New Laws, issued in 1542 by Charles V, which forbade the treatment of indios as slaves- they could be asked to pay tribute but if forced to work had to be paid for their labor and could only be forced to work for limited periods. The New Laws also initially established that encomiendas could not be inherited- as grants from the crown they would revert to the crown upon the owner's death to be redistributed to another loyal Spaniard.

But the New Laws did not have the intended effect. From New Spain, the King essentially received the infamous reply "obedezco pero no cumplo" (I obey but I do not comply)- as the Viceroy believed that the New Laws would devastate the economy and cause a rebellion against the monarchy. The viceroyalty instead slowly instituted the requested changes and avoided the bloody conflict that occurred in Peru. The Viceroy of Peru was murdered during a rebellion led by Gonzalo Pizarro, and although the rebellion was defeated and Pizarro executed, exploitative labor practices were there to stay.

Which brings us to the next point, that encomiendas did not function the same way throughout the New World. In New Spain, the former subjects of the Aztecs were used to paying tribute, and so the closer that the encomenderos kept to existing systems of tribute, the smoother everything went. Depopulation from disease, however, meant that incomes from tributes decreased, and other ways to amass fortunes were needed- so haciendas (territorial possessions worked by a mixture of forced labor, paid labor, and slaves) became a better option than seeking out an encomienda. In contrast, the Inca had a system called the mit'a, based around temporary forced labor by subject peoples. Initially, the mit'a was represented a commitment that each ayllu (kin group) would send one out of seven of their men each year to do paid labor in service of the empire, and later of the Spanish encomenderos. But again, with the devastating depopulation (and many indios fleeing from their ayllus to avoid being conscripted) the demands for tribute labor fell on fewer and fewer people. Also, in Peru, the conditions of labor were more dangerous, as many of the forced laborers ended up in the silver mines at Potosí or the mercury mine at Huancavelica- in both cases, the workers suffered from mercury poisoning and lung problems and many died during or soon after their period of labor. Nonetheless, some stayed on or even moved to the mines in search of work- as the source of forced laborers dried up, paid labor became more prevalent.

Encomiendas were not officially abolished until the end of the colonial period, but by that point they had virtually disappeared in favor of less coercive, and ultimately more profitable, labor systems. It was legally distinct from feudalism, and legally the indios were more free than serfs or slaves, but in practice the system was more prone to abuse, due to the local power of the encomenderos relative to permissive Viceroys and a distant king who might try to better the conditions of his subjects abroad, but at the same time was disincentivized to do so by the unprecedented flow of silver back across the Atlantic.

It should be noted that the issue of defining feudalism is quite controversial, even in its original European context. There was a very informative AskHistorians AMA about this topic a couple of years ago, which includes a discussion about its applications to areas outside of medieval Europe. There was also an exchange between /u/400-Rabbits and /u/TheGreenReaper7 about its use in Mesoamerican studies.