I have introduced Maimonides in a previous post. Nahmanides was born in Girona, then part of Christian Spain. He was a mere child when Maimonides passed away, but in his adult years was embroiled in the controversies surrounding the supporters and detractors of Maimonides. He was heavily influenced by Maimonides' thought, but rejected his extreme rationalism and allegorisation of miracles. Here I'll let Josef Stern present one of the differences between their views.
We know what Maimonides thinks is wrong with idolatry. Even if the idolator does not believe that the idols themselves, the artificial icons, have power, he believes that they are images of gods or celestial beings who are worthy of worship because they have power over humans. In fact, however, Maimonides argues, these purported beings are powerless or unreal. Therefore, their worship is based on a false and empty presupposition. What is fundamentally wrong with idolatry, then, is that it is founded on a cognitive error of the highest magnitude (Guide of the Perplexed, I:36:82-83).--Josef Stern, Problems and Parables of Law: Maimonides and Nahmanides on Reasons for the Commandments (Ta'amei Ha-Mitzvot) (Albany, New York: SUNY Press, 1998), 144-145.
For Nahmanides, in contrast, what is wrong with idolatry is not that it is based on a false presupposition about its objects of worship.
Just the opposite: idolatry is forbidden (to Israel) precisely because its objects are real entities and powers.
In his Commentary on Exod. 20, 3, Nahmanides describes an elaborate metaphysical hierarchy, consisting of three classes of celestial beings each of which has dominion over certain peoples and places on earth, ranked in an order of power that also corresponds to the chronological order in which their representative kinds of idolatry historically emerged. The first, highest, and earliest objects of idolatry were the immaterial separate intellects, or angels. Some of these were originally believed to have power over specific nations and were therefore worshipped even when their respective nation recognized that there is a deity superior to them. Israel, however, was absolutely forbidden to worship any of these angels because it is the specially treasured people (segulah) of God who alone has power over them. Were the people of Israel to worship these “other gods” [‘elohim ‘aherim], it would be tantamount to a rejection of the one God for the others.
The second class of objects of idolatry were the visible heavenly bodies:
the sun, moon, stars, and constellations who were also known to have power over specific nations. Unlike the idolatry associated with the first class, this second kind was also theurgic: by worshipping their respective star or constellation, its worshippers believed that they could strengthen it and help it "victor" over its rivals, thereby improving their own fortune. These idolators were also the first to make physical shapes and idols whose timing was astrally significant. Through this elementary form of astrology, this brand of theurgic idolatry came to be associated with magic and to include the worship of certain humans whose power seemed closely linked to constellations.
The third species of idolatrous objects were the demons [sheidim], a class of spirits [ruhot] who, Nahmanides claims, are so-called because they dwell in destroyed or desolate [shadudim] places (C Lev. 17, 7).
These devils are material but invisible, compounded of fire and air, an ontologically intermediate kind of being with some angelic and some human properties. Thus they eat and drink, especially blood; decompose and die; fly and inhabit the sky; and know the near future (news of which they overhear from higher celestial beings). Like the higher powers, they are also assigned to specific peoples but with dominion only over ruined, wild places where they are empowered only to harm enemies and those who fall victim to them. Nahmanides treats these devils with some contempt, as nouveau deities who lack the power to benefit their worshippers, who were not worshipped by the ancients, and who were "discovered only by late Egyptian magicians. Yet he thinks that they are no less real than the others. Indeed the most important point about all three classes of objects of idolatrous worship is that they are all real beings with real power- which is precisely why they are forbidden to Israel who is commanded to worship only the one God.