Well, this is quite a difficult question to answer, mainly because we don't really have good figures for the amount of ceremonial violence in Mesoamerica, and what evidence we do have is either highly biased, or localised to specific areas. This makes any comparison with Europe difficult. However, it is certain that the image of the Aztecs (really Mexica) has been distorted, making them appear more violent and savage than they really were.

The massive exaggeration of sacrifice is a big problem, and one that goes back to early Spanish sources. Conquistadors such as Andres de Tapia and Bernal Diaz reported seeing skull racks with hundreds of thousands of skulls (in different racks, of course). Diego Duran even once claimed that the Mexica sacrificed over 80, 000 people in one ceremony. However, it is worth point out that very little archaeological evidence for sacrifices of this scale, and in the most extreme cases, the reports stretch credibility. Other sources suggest that the Mexica had much smaller sacrificial needs. The Florentine Codex (specifically Book 2) suggests that the Mexica sacrificed far fewer people a year. Caroline Dodds Pennock in ‘Mass Murder or Religious Homicide? Rethinking Human Sacrifice and Interpersonal Violence in Mexica Society’ suggests that between 300-600 people were killed in ritual violence, and I think that even this lower figure may be a touch too high. Furthermore, Mexica military objectives were much less captive orientated than is commonly believed. For example, many people will reference the 'Flower Wars,' as an example of Mexica barbarity, fighting wars just to take sacrificial victims. However, scholars such as Ross Hassig and Barry Issac have argued that the Flower Wars were actually a strategic tactic, intended to wear down a tough enemy, or even an excuse for the Aztec's inability to defeat a 'weaker' rival. An additional belief is that the Mexica demanded captives as tribute. But this isn't really true. The Codex Mendoza shows that captives were not really included as tribute. Only 1 province sent captives, and only in small numbers, every now and then. This indicates that captives were not really a priority for the Mexica at all.

Furthermore, Mexica ritual violence is often taken outside of its political context. There were only a few hundred thousand Aztecs trying to rule an Empire of millions, and the entire Postclassic was a turbulent period, full of wars, rebellions, and assassinations. Outnumbered and surrounded by unreliable allies, ritual became a tool of state. The Mexica were known to invite neighbours, allies, vassals, and even enemies, to witness their ceremonies. The idea was to display Mexica wealth and power, and possibly to intimidate others. These events also served as an opportunity for networking, creating a system of patronage centred on Tenochtitlan. Lastly, the Mexica were devout, and so their offerings to the gods were intended to bring prosperity to the land. By showcasing these performances, they could claim that they were restoring fertility to the land for all, justifying their rule. It doesn't help that the logic behind human sacrifice is often unknown, or else distorted, and so people don't have a good understanding of 'why' Mesoamericans sacrificed people, and this creates the impression that sacrifice was arbitrary brutality, when it was actually connected to deeply held beliefs about spiritual exchange.

The violence itself is also exaggerated or misunderstood. Sacrifice was not really a punishment or a torture (though some rituals could be very brutal), and in most cases death was quick. Captives were generally well treated and some even lived with the people who captured them, and were mourned by their hosts when dead. Many rituals required the victim to actively participate in the ceremonies that would kill them. Remember, the victims usually (though not always) came from the warrior class, and so believed that a sacrificial death was an honourable fate. This isn't to say that sacrifice is a good thing, but compared to ritualised torture practised in Europe it is hard to argue that it was any worse. Not that we should distort or exaggerate the level of violence in Europe either (they had their reasons too), but at least the Mexica got to go out with glory, and their dignity intact.

I think the problem is that Aztec human sacrifice ticks all the boxes for what Europeans understand to be 'bad'. There is a lot of blood (Europeans have something of a cultural 'blood phobia'), it targets 'innocents' (not really. But the stereotype of a virgin sacrifice is pretty strong), the presence of cannibalism (conveniently forgetting about corpse medicine), and its dedicated to 'pagan' gods (worst of all). Note how Spaniards such as Hernan Cortes and Bernardino de Sahagun often praise draconian Mexica laws and violence when it is secular and directed against 'undesirable'.

It doesn't help of course, that Aztec beliefs and social values are not well known among the general public, and so this leaves the 'violent Aztec' as the only representative of their culture to the modern world. It is telling (though not surprising) that as people learn more about Mesoamerica, they tend to view Mesoamerican's more and more fairly then people who only know a little.

Sources:

Berdan, Frances F. and Anawalt, Patricia Rieff:

• The Codex Mendoza Volume I: Interpretation, (Berkeley: University of California Press, 1992)
• The Codex Mendoza Volume II: Description of the Codex, (Berkeley: University of California Press, 1992)
• The Codex Mendoza Volume III: Facsimile, (Berkeley: University of California Press, 1992)
• The Codex Mendoza Volume IV: Translation, (Berkeley: University of California Press, 1992)

Berden, Frances F. et al.

• Aztec Imperial Strategies, (Washington D.C.: Dumbarton Oaks, 1996)

Cortés, Hernan:

• Letters from Mexico, tr. Anthony Pagden, (New Haven: Yale University Press, 1986)

Díaz, Bernal:

• The Conquest of New Spain, tr. J.M. Cohen, (London: Penguin Books, 1963)

Durán, Diego:

• Book of the Gods and Rites and The Ancient Calendar, tr. Fernando Horcasitas, and Doris Heyden, (Norman: University of Oklahoma Press, 1970)
• History of the Indies of New Spain, tr. Doris Heyden, (Norman: University of Oklahoma Press, 1994)

Hassig, Ross:

• Aztec Warfare: Imperial Expansion and Political Control, (Norman: University of Oklahoma Press, 1998)

Issac, Barry L.:

• The Aztec 'Flower Wars'': A Geopolitical Explanation, Journal of Anthropological Research Vol. 39 No. 4 (1983)
• Aztec Warfare: Goals and Battlefield Comportment, Ethnology Vol. 22 No. 2 (1983)

Kerkhove, Ray:

• ‘Dark Religion? Aztec Perspectives on Human Sacrifice’, Sydney Studies in Religion (2008)

Pennock, Caroline Dodds:

• ‘Mass Murder or Religious Homicide? Rethinking Human Sacrifice and Interpersonal Violence in Aztec Society’, Historical Social Research/Historische Sozalforschung, 37:3, (2012)

Sahagún, Bernardino de:

• General History of the things of New Spain Book 2: The Ceremonies, tr. by Arthur O.J. Anderson O.J., and Charles E. Dibble, (Santa Fe: University of Utah, 1979)