Well. Both are like twin towers. They both have innumerable positives.
The good thing about Maya is that it makes you versatile in interacting with high-end programs like Houdini which is purely based upon maya basics. But has another way of making stuff. Like born in america and living in england. Get the difference?
Comparing the advantages you get with maya, There are lots of tools to create stunning results. Say FumeFX, Realflow, Dreamscape, etc; These all are standalone cm plugins or say Third-party tools which you need to require to get advanced effects for Max. Whereas Maya have them in-built in their style of generating fluids and particle effects. Say whereas Max has NURBS for modeling, but it really sophisticated to use, But Maya has a well developed NURBS Modeling, say interface. Max requires a lot of third-party tools to equip to get like maya like arsenal.
But the power lies in animation. Maya is specially known for fun, exciting way to animate things. I've personally done myself some and compared to MAX, where you need to have the complete details of the modifying tools, Maya is like an assistant to your creations if you get around with the tools it has. It does the rest when you just need to do the basic things. Just like Reactor in Max, for example. There are many more like it in Maya.
But i think once you get a good idea of any one of these Powerful software, then it's not hard to get adjusted with the another. Yes, takes time though but there's where you can get to know the differences between the two. Like Max has a thing that's easier to do in Maya, or maya has something that is greater compared to Max.