Maya dominates film because it was originally a unix suite and everyone in fx was using SGI machines. Now a days it's for different reasons, but being able to work on unix is a big reason since most fx houses use Renderman. Max doesn't play well with either unix or Renderman so it's use would be limited to most big fx studios.
Max is a more and more capable product now for film, although it's built in particles and character tools could use some work to compete with Maya and Xsi in those areas. Modeling rendering and rigging are not that far off in Max in recent versions.
From a business stand point I don't think Autodesk worries since all three products are under one roof. No sense making Maya better for Arch Viz or Max better for film when you already have products that fit the bill. I am a Max user mostly and for Arch Viz or games I generally prefer Max, it's the better modeler and with great Vray integration it is my tool of choice for those areas I focus on.
Blender is a bit of a work in progress right now, but for free is catching up quickly to the big boys. Being open source it's developers can't have the sort of focus a commercial team can I guess, but it's sporting some pretty cool features.
Cheers
Mike K
