They are very different when it comes to how they function. Max uses a modifier stack, where you are stacking a modifier on top of another, on top of another, and so on to apply changes and manipulation. Max also has the implicit differences between Mesh and Poly, which I still find confusing and I've been working with it for a while now. haha

Maya's implementation is all node based and you are able to manipulate the deformation order to your liking. I also find it a lot easier to grasp and more user friendly. That's just my opinion, though.

Both programs are very viable applications, with pros and cons, strengths and weaknesses. There are lots of things about Max I like and lots of things about Max I hate. Same with Maya really. I personally just prefer Maya's workflow.