Rotate object "Like Center Mouse Button" (I don't even know how to articulate this). 

Say I start Blender with the default 2d scene - cube and view centered at 0,0,0. I can use the center mouse button to rotate/pan around the cube. Any up/down mouse movement gives me a "pitch" with respect to local view, and any left/right mouse movement "yaws" the cube. The amount of movement is uniform no matter where my cursor is, and no matter how I have rotated the other axis. This is an easy and natural way to pan around an object.

So now I basically want my camera do to the same. The best technique I've seen is to create an empty at 0,0,0, parent the camera to that - view through the camera - and rotate the empty.

That works - but no matter what I do - I can't get the same kind of rotational control with my mouse that I had with the "center mouse button" above. I've tried everything from changing the rotate transform mode (global, local, view), locking one of the axis, and using rr for "trackball" mode. 

I can almost do this if I use the gimbal in "view" mode and just move the up/down and left/right rotation handles (individually) - but the mouse behaves very poorly - like it gets too sensitive near the center of the gimbal, and stops working altogether outside of it (giving a very narrow, single-axis control, oddly-proportional control). Nothing like the two-axis control which is completely linear - even if you indefinitely move the mouse in one direction. 

Anyone know how to do this?
You can move the camera exactly as your would move the viewport by just enabling "Lock Camera to View" in the view section of the properties panel (n), and then move your viewport: your camera will automatically follow.