Asking that question has started more flame wars on forums .........
The truth is there really is nothing that can be done in one that cannot be done in the other. It is just the steps involved to get the same result. I use 4 different applications, Max, Maya, XSI, Houdini . They all have their strong points and some things in one application are easier to do than others. Houdini is great for particles, really nothing compares, but terrible at modeling. Max has better modeling tools but Maya is better at dynamics like cloth. XSI is strong in visual effects and with the release of ICE it can produce some great effects.
OS is another factor. Max is windows only. Maya is windows, linux, Mac. Xsi is windows and linux. For me I am looking at moving entirely to XSI. I was not happy with the last release of Max. It has become severely bloated as an application and the workflow is starting to get hampered by that. Maya and Max really need a rewrite . They both are based on software that has simply been added onto each version to the point there is so much code there that its becoming inefficient. But they want to keep old and new users happy.
XSI did a total rewrite about 3 years ago and it has made all the difference. They have the trial version released for any interested. Trial link is on the side. Try it out and see if you don't think the interface and usability is much more in tune with modern pc.
http://www.softimage.com/products/xsi/
After downloading and installing go to file open scenes / ice, open the examples like simple fire and press the play button at the bottom. That is fire rendered in real time.