So I broke down and grabbed a DS3 from ebay. I needed a second controller, and I had to play DMC4 with rumble. Very glad I went for it. $52 plus $15 EMS shipping from Japan had it in my hands in 4 days, and it's worth every penny.
It's a shade heavier than the sixaxis, but even with a sixaxis in one hand and a DS3 in the other there isn't an obvious difference. I forget how much heavier the DS2 was, but you could pick up a DS3 and think it was a sixaxis very easily. However the build quality is night and day: the DS3 seems much more robust, and that makes the sixaxis feel a lot less significant in the hand by comparison, even if both weights are comparable.
There are also some subtle but obvious improvements to the DualShock design. As others have noted, the triggers are tighter and feel slightly more satisfying to press. But am I alone in thinking the D-pad feels far better on the DS3? I never had a problem with the DS2 or sixaxis D-pad, but the DS3 pad feels fantastic. There's a satisfying sense of clickage with all eight directions, as if the controller is confirming the diagonals when you press them. I get a much greater sense of feedback to my thumb from the pad. I haven't tested it with any games yet, but it seems like a huge mechanical improvement.
Rumble feels tighter than it did in the DS2. I've only tested it with SSHD, and I can't tell if the DS3 is capable of a greater range of vibrations from my limited experience. However, the motors do feel much more integrated into the controller this time around - more like the 360's pad - and compared to the DS2, it does feel like a true step up. Thinking of which, some have said the DS3's rumble is weaker than the 360s. I couldn't tell, though I had been playing Gears that morning and didn't subsequently feel the DS3's vibration was lacking. But it's definitely a different rumble. Not better or worse; just a very different tactile experience.
Overall I'm surprised by how impressive the new pad feels. I expected a DS2 in a sixaxis shell, but the DS3 feels like a genuine redesign. I'm certain there have been some subtle changes that make for a significantly improved controller. If only those changes had included proper triggers.
Edit: I can't comment on any improvements to the bluetooth signal dropouts yet. I haven't used the DS3 enough, and since I very rarely experienced the problem with my sixaxis I'm not the best person to discuss the issue.