I've done South Kaibab to North Kaibab to South Kaibab, mainly becasue I didn't want to deal with a shuttle.
I've never done Bright Angel.
I know most runners seem to like going down South K. and then back up Bright Angel at the South Rim. There's no water on South Kaibab and there is on Bright Angel, but not a big deal to me, it's only ~7 miles from river to rim either way.
Personally, I'd prefer South Kaibab round trip just because it's what I know. Yes, it's pretty steep (but what isn't out there?), but to me it's a known known, making it easier to get my head around. Bright Angel, for me, is currently a known unknown...
"We know there are known knowns: there are things we know we know. We also know there are known unknowns: that is to say we know there are things we know we don't know. But there are also unknown unknowns — the ones we don't know we don't know." —Defense Secretary Donald Rumsfeld