If it didn´t change yet, the big problem with bullet is the basicly missing documentations and examples that rely heavily on inheritance in a way which makes them hard to understand. At least if you want to go further than basic rigid bodies. Newton is just great but as far as I know it is still rigid body only? On the other hand, there is hardly much use for the other stuff. On the other hand Crysis is a good example for some softbody like physics on plants and I also like the idea of bursting wood without predefined places .
What people currently seem to tend to forget is Havok. The physics simulation is nearly as clean as Newtons, but it is quite a bit faster and has stuff like softbodies aswell since some time.
PhysX is pretty fast as well, but the physics are less stable, but thanks to all the documentation and the fact that it is free, it fits many projects quite fine.
But I have to say that these are experiences I made two years ago, so things may changed a lot actually .
I will use bullet for my iPhone engine, as I love its license, which basicly allows me to do everything with it for free, as long as the sourcecode keeps the license header