Lightwave has fur / hair, physics and cloth-simulation included. Lightwave is a complete software for modeling, animation and rendering. It is very stable (especially compared to Autodesk products).

Maya is also a good software. The animation tool is told to be better than Lightwaves animation especially in terms of character animation. Both can do the same but Maya can be a bit faster in this area. In terms of modeling it is hard to say. Lightwave is very fast if you know how to use it. And the material editor of Lightwave is the best in the entire CG world.
The price of Lightwave is only a fraction of Maya.

Exporters are available for Lightwave. There are exporters for Gamestudio (from Greenbriar Studios), for Torque (David Wyand) and two exporters for Ogre. I have no idea about Dark Basic.
It can also export to FBX, Collada, obj and 3ds. There are plugins available for many other formats (e.g. X).
I don't know about the Maya exporters.

If you want to do pure modelling then Modo is indeed a very good option, more modern than Lightwave, 3DS and Maya.