3DS Max definitely exists. Autodesk is still supporting them, and not as a 'oh this is just an auxiliary side project'. The breakdown (oversimplified) is Maya is more for complicated models used in animation/CGI (MEL scripting is their 'killer' tool that puts it ahead of Max), while things like architectural and game models are mostly done in 3DS Max (but theres a lot of overlay between the two, i.e., I've seen tons of work done in game modelling on Maya LT).
Speaking of which, Maya LT is not that badly priced for what you get - I have no animation ability but I've seen my friends do some incredible things with it. If you're artistically inclined, have a play. Regardless, the lack of Blender support makes me sad.
