Best modelling program for Amnesia?

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No, you can get a non-commercial license for free if you're a student.

Now the thing is, both programs are very powerful tools, so there's almost nothing you can do in one tool that you couldn't also do in the other one. I've worked with both programs for two years now, using Max mainly for modeling and Maya mostly for rigging and animating. I'd say they're both equally hard to learn...maybe Max is a little bit more intuitive but not much.

Quite frankly, once you've gotten the hang of the whole 3D thing, it's actually just a matter of knowing where the buttons and functions are, because most modeling programs work very similar at the core and most functions can be found in every program (they're just sometimes named a bit differently or hidden somewhere else). So what I'm saying is, once you know one of them, you can learn the other one pretty quickly, too. It's not a choice for life which one you start with, unless maybe you're a VERY slow learner.

Now the biggest difference between the programs (in my opinion) is, Mayas scenes are entirely node-based. This doesn't really matter that much as long as you're just modeling, but it becomes VERY important once you start rigging, because it makes it a lot easier to create cool control rigs by connecting nodes wih mathematical operations and whatnot. (You may be thinking "WTF?" now, but if you dig into rigging a bit you'll see what I mean )
Mayas Animation interface (Graph editor etc.) is also less cluttered and easier to use than Max's and it has some cool functions Max is lacking (Infinity animation curves for example if I'm correct...haven't animated in Max for a while.) So that's why Maya is my choice for rigging and animating.

Max on the other hand is more intuitive in the modeling departement, especially with the addition of the Graphite modeling tools in the 2012 version (or was it in 2011 already?) and with the possibility of stacking modifiers onto each other. Maya is for example still lacking the possibility of having several symmetry axes on your model while you work. The Graphite modeling tools are also great for doing retopo (= creating an optimized lowpoly on the surface of a highpoly) and they have other cool functions that make modeling a bit more comfortable overall.
Another great strenghth of Max is that you can easily implement realtime viewport shaders like Xoliul or 3Point shader to give you a preview of what your model might look like in an engine. (Rendering your real time model with mental ray or whatnot doesn't tell you anything about that )

Also, if you're planning on working in the games industry one day, I wouldn't recommend using Blender. From what I've heard it's pretty damn good for a free program, but I've yet to meet a studio that actually uses it. Most are using Max or Maya, sometimes Modo, Softimage or Cinema4d.

Btw...That article there seems a bit weird to me...it lists features like "Manipulate each individual vertex" for Maya as if Max didn't have that too...and leaves out much more important features. Besides those are such basic features, EVERY 3D program has them. (How could you model something without being able to manipulate vertices?!)

The problems of exporting can not exactly be worked around

Hm...I've read somewhere that there's a seperate little tool that can convert fbx files into the collada format. Just out of curiosity, have you ever tried exporting fbx from max and then using that?