Maya seems to be a good candidate for this, especially because it offers the perspective skewing with the camera when running/zooming forward. The drawback is that it is quite a bit of work and the camera cannot be edited independently of the scene post-render.
AE on the other hand can create a wiggle expression to emulate camera shaking. It can be edited independently of the scene which is nice. It is a simple jutter though, so it lacks the perspective skewing of a real 3D camera.
Any recommendations on which option to go for? For extended scenes with a lot of shaking, have you noticed a considerable difference when either of the two methods are employed?