3DS Max

Maya is a proprietary scripting language. MEL is highly customizable, and that is one reason why Maya can be found a lot in the film industry because studios like to be able to create their own set of tools that can help them achieve their job much easier. Maya has really been know as the go-to app for 3D animators in the industry for its robust rigging and animation tools and its animator friendly workflow. You also have the choice of Maya LT which is a huge benefit among new game developers as it's a relatively cheap subscription cost, of course, you don't have access to as many of the features of the full version of Maya, but you still have the most important to a game designer, like modeling, animation and texturing.
Where 3Ds Max shines:
3Ds Max has been known for its powerful modelling tools, allowing you to create complex 3D models with a very fast workflow and robust modifiers, with the entire poly modelling tools contained in one area of the UI. It also has some really great architectural visualization capabilities that Maya really doesn't have. If you're brand new to CG 3Ds Max can be a little simpler to grasp, and can seem a little less daunting than Maya, making it a bit more user-friendly.
The big factor:
The biggest factor in choosing between the two actually has nothing to do with the application's toolset, but your operating system. Maya is available for Windows, Linux, and OSX platforms. 3Ds Max, on the other hand, is only available for Windows operating systems, which means if you're a Mac or Linux user, 3Ds Max is probably not the best choice.
The verdict:
You should really know what you're going to use the app for because this can help you decide which program to choose, and each program has different strengths when it comes to the different tasks, like modelling, or animation. If you want to get into character animation, Maya may be the best choice. However, 3Ds Max still has great animation capabilities, but Maya has a slight edge over it with its deeper list of tools. When it comes to modelling, either software is going to get the job done; it really comes down to which workflow you like more. 3Ds Max has a robust modelling toolset, but Maya has recently enhanced their tools as well. 3ds Max has typically been seen as the 3D app for the game industry, and it is known to have a bit more flexibility and options. However, Maya LT is also a great cost-effective choice when it comes to game development.