Gmax was limited to game companies that produced and licensed plug-in exporters. This seriously hurt the product, as no-one wanted to invest in this. You can still download it from Fileplanet (Gmax 1.2 with Quake3-Engine Exporter Set "Tempest") but personally I'd recommend downloading 3D Studio Max (30-Day)Trial Edition. Basically it's the full thing you get to use for 30-Days, then you either buy it or uninstall it.
Unfortunately Maya and Softimage|XSI don't have that, instead they have full versions that are limited to what they export. Both are quite popular still because XSI supports Half-Life 2 (so is quite big with that community) and Maya supports Unreal 2.x/3.x (so is quite popular with that community).
I would say purchasing a 3D program comes down to preference if you don't have to use it for your given profession.
As far as the differences between Maya and Max go, while technically yes they are both owned by Autodesk .. they are still entirely autonamous companies who are owned by a larger corporation.
Discreet still develop 3D Studio Max
Alias still develop Maya
If they didn't then they'd end up loosing that individualism that people prefer from each. The industry seems to swing on what is popular based on who creates a stunner heralded game with each one.
This said, that generally only applies to the "bottom-end" of the development barrel. It is quite rare for established developers to change their art and programming pipelines without a damn good reason.
Maya has been and still is the industry standard for game development. With longer and more complex pipelines this isn't going to change any time soon either.
Reason behind this is quite simple.
It allows developers to do artwork very quickly. This is the reason why I prefer to use it to anything else.
In each of the other products I've tried, atleast one aspect of development has been difficult to deal with. Causing pipeline slow-downs. With Maya, while it doesn't have the largest toolset in the world to work with.. what it does, it does right!
I've found that in other 3D apps (Max, XSI, Houdini, Lightwave, TrueSpace) it can take me the better part of a week to create a single model from concept to finish.
With Alias' range of products, this pipeline is very quick and small. I can concept in Sketchbook as I would with pencil & paper, then pretty it up with colouring you'd expect from Coral Painter (which crashes ALOT). After that it's fairly simple to get in to Maya create the base mesh within a couple of hours, then I can generally rig ANYTHING within another hour; especially with the auto-bind. Makes finding animation issues with the mesh and changing them so damn easy and quick it's a god send. Once that is done it's fairly simple to wrap models as you don't have to do it all seperately. You can unwrap in both the 2D window and 3D perspective. Once the base texture map is there, I can then move over to Ashli + FX Composer for DirectX-compatible shader development. This all integrates perfectly so I can see changes in real-time as I'm making them. It means that I can get things looking and running exactly how I want them to.
I can then tie-in Photoshop for the colouring and design of the textures to ehance what the shaders are doing, again this can be integrated so real-time changes are possible to see.
Maya fully supports displaying DXT and HLSL. This means WYSIWYG in terms of DirectX development. As Maya also works by default to a 1:1cm scale, it also means that while yes engines like Half-Life 2 are out of scale.. Doom3, Unreal Engine, and DarkBASIC Professional there are no translation problems. In-fact it's a 1:1 scale with DBP.
With Aegis PhysX plug-in you can also incorporate full physics animations in to your scenes. Everyone else seems to use their own custom solutions from Havok, but I really like the Aegis system as it's a sinch to use and integrate. (oh did i mention it can output the physics models too?)
Because of integration you can also utilise both Shake (Mac) or PremierPro (Win) to export and edit rendered movies.
All of this thought will usually take me a couple of days rather than weeks to get a model from concept to in-game. Also means that if a major overhaul is required, then it's very simple to do that.
The BonusTools Alias release with each edition (mostly to show off new scripting abilities) generally help greatly for game resource development. BonusTools 6.5 for example are almost invaluable for creating buildings or terrain.
Something I've found personally invaluable that only Maya has, are the layers. Most apps have groups, and objects.. Maya has those too, but Layers allow you to create in a similar way you would say in Photoshop. You can build-up and affect each one as you need to.
So let's say you wanted a higher polygon model for movies, than in-game. All you would need to do is have the model (and it's resources) in one layer-group, then create an instance layer group based on it. Set a mesh-cage around your model, map the lines you want static (basically like saying what MUST remain as the outline for setting harder edges) then sub-divide.
As the layer is an instance, there would be no physical mesh; that would be you're game mesh. Instead what it does is add the changes you made, which you can check the undo-queue to change between point. So you animate the model, or use currently made animations; and rather than having to re-rig for the new model all you do is click to show the layer and bam .. you have you're high-end version with very little effort.
What is cool about Maya, mainly is the fact that the learning curve is so gentle. All of the tools have enough options to keep the professional happy, but you don't have to access or use them if you don't want to. It's that scalability that makes it so good at every level. What's possibly even better when you learn MEL is that all of the plug-in's loaded you can access with MEL. This means if a tool does *almost* what you want it to, you can always code up a short-cut with an option menu for it to do exactly what you want to.
At the end of the day it's your decision, and given the size of the purchase it might come down to how much you're willing to stretch your wallet.
I just suggest you think seriously and try each one out. Make sure whatever you do get, you're happy living with.