I've heard arguments about heavier cameras being easier to handle under some circumstances (i.e., more mass == more inertia == less jiggles), but it's hard to beat a light travel weight.
When I went from my Canon G3 to the Nikon D70, the big change was giving up on the rotating screen. Initially it bummed me out, but then I made up for it with the frame rate. On the G3, pressing the button was a big commitment. It takes several seconds to commit an image (in raw mode) to the memory card. On the D70, it's all nicely buffered so you don't have to worry about it. That means you just hold the camera in whatever position, shoot a few shots, and check to see if you ended up with what you had in mind. This works pretty well for normal lenses, but has proven to be insufficient for my fisheye lens. Every small bit of tilt in the camera can have a radical effect on the final image and you really have to be seeing the final image to get it right.
So far, the Fuji S3 and the Canon 20Da (the "astronomy" version of the 20D with the infrared filter removed) have introduced LCD preview modes, but it's not clear that either would be useful in practice. If you like being eccentric, you can get it today in the
Epson R-D1. Presumably, as the D-SLR space gets more crowded, the flip-and-rotate screens will start showing up in more cameras. It's a great feature.