=== Autodesk 3D Studio Max ===

Features on 3D Studio Max:
- MAXScript (for automate repetitive tasks)
- Character Studio (for animate virtual characters)
- Scene Explorer
- DWG Files Import
- Texture Assignement/Editing
- General Keyframing
- Constrainted Animation
- Skinning
- Skeletons and Inverse Kinematics
- Integrated Cloth Solver
- Integration with Autodesk Vault

Films have made use of 3ds Max:
- I, Robot
- X-Men

Price:
$3,495

=== Autodesk Maya ===

Maya was developed by Alias and Wavefront. On January 10, 2006, Autodesk completed the acquisition and now known as Autodesk Maya.

Features on Maya:
- Maya Fluid Effects
- Maya Classic Cloth
- Maya Fur
- Maya Hair
- Maya Live
- Maya nCloth
- Maya nParticle
- MathMover
- MEL Scripting (Maya Embedded Language)

Film have made use of Maya:
- Ice Age: The Meldown
- Geng: The Adventure Begins
- Monster vs Aliens
- James Cameron's Avatar
- Jurassic Park
- The Abyss
- Therminator 2: Judgement Day
- Dinosaur

Price:
$3,495

=== Personal Comments ===

3ds Max is the most famous in gaming industry while Maya is in film/TV industry.

Both of them are very pricey, but free trial version is available. Or you may use these free alternative softwares:
- Blender 3D, http://www.blender.org/
- Google SketchUp, http://www.sketchup.com/
- TrueSpace, http://www.caligari.com/

Blender is the most feature-rich among all the free softwares above. SketchUp is the easiest, it's so easy, you maybe no need to learn. But it's only for modelling, does not support animation. TrueSpace is pretty nice, but the development has been stopped since 2008.

Which is the best (or better)?
Depends on what you want to use it for and how much you're willing to pay.

For general purpose or easy to find a job, choose Autodesk 3D Studio Max.
For create an awesome film, choose Autodesk Maya.
For doing freelance job and save your money, pick Blender.
For introductory and playing the 3D, take SketchUp

In the past, Maya and 3dsMax were direct competitors towards the same demographics and providing comparable functionality. 3dsMax has been considered something of a learning software in the past, and maintains a 'student edition' like the Adobe tools.

Now that both programs are owned by Autodesk, both are used in mainstream, high quality game and movie products, and both support advanced effects, the difference will come down to interface, output, and specialized feature sets, like texture modules, etc. Testing both trial versions will give you a sense of these, and preference probably will differ from user to user.

I searched for contemporary discussions, and it seems that, like in the past, 3dsMax is generally regarded as both a legitimate production software and a student tool. Maya is not marketed toward students as often, and is also featured in high-profile, large budget projects.

According to a DigitalJuice.com thread, both programs retain the steep learning curve they have always been known for --- but some users consider this less of a problem with 3dsMax. The same users also considered Maya slightly higher-end.

Through legitimate means, a cheaper version of 3dsMax is available than of Maya. Any search for a student edition will bring similar results to student versions of Adobe products