I posted this in another thread in response to someone, and a few others have asked me for a comparison as well, so here you go... grain of salt and all. Oh, and for what it's worth, some of this applies to the Razr as well, given the similarities between the Razr and Bionic.
Hard to say - I haven't had any major data drops on the Rezound. But honestly, the Bionic has been just as good, at least since I got the Rezound. I've seen a couple of brief hiccups, but never lost data for more than, maybe, 30 seconds as it was going between 3G/4G. Plus I keep switching my SIM between the two to try out different things. I'm not seeing near the reports of data drops on the Rezound, but I'm sure not near as many people have it yet either... no good answer on this one yet. There have been a couple of times where the Rezound grabbed 4G in places I don't believe the Bionic ever did, but that's a really hard thing to judge since clearly this LTE network has its good and bad days.
The screen on the Rezound is impeccable. It's harder to read in sunlight outside than the Bionic, and the Razr falls somewhere in between in that regard, but man it looks good. The true, accurate RGB LCD, plus the high resolution, it's just beautiful. I think it has 342 ppi? Or 324? Can't remember, but it's the highest on the market now (higher than iPhone).
Call quality, sound quality, etc are about the same between the two - great. Beats is nice, but not that big of a deal when you mess with the "media effects" on the Bionic. I almost give the Bionic a one-up on this (and the Razr for that matter) b/c at least their effects are system-wide, as opposed to only the stock music app on the Rezound.
The Bionic seems to get better battery life, which is not a huge surprise. The Rezound is good though - it idles really well. Definitely improved since the Thunderbolt. The Bionic is also thinner, but the Rezound is very ergonomic and feels really good to hold - but that's a personal preference thing - and even I go back and forth on which I enjoy more in that regard. Could be nostalgia as I was a huge DX fan, and the Bionic feels a bit like that at times.
Rezound camera blows the Bionic's away. Not a surprise, HTC makes great mobile cameras. Given time and good light, the Bionic can take extremely good pictures. But the smoothness and speed of the Rezound's camera, plus it's ability to take decent pictures in the dark (not as washed out by the LED anyway), it's just much better.
Speed... The Bionic definitely feels faster/snappier to work with. I'm a fan of Sense, always have been, but you can feel it weighing things down at times on the Rezound. A few little jerks here and there, the occasional slight lag. It's nothing major, but for a change, a Moto phone actually feels smoother and snappier than an HTC. Now, give the Rezound some custom ROMs and some optimizing, and I would imagine it would be on par with (if not better than) any phone out there. I also remember with the HTC Sensation 4G, it's first run had a bit of choppiness, but after they pushed out a maintenance OTA to help with a few things (including that), it was much better. So this could, theoretically, easily be fixed.
That's probably more than you wanted to know, but there you go. They're such different devices and different experiences with different pluses and minuses, it really comes down to preference. Now, if the data drop thing shows itself to be a Moto only issue that the OTA doesn't patch, then I'd say Rezound hands down. But if that issue is about the same across the board, then pick your poison!