I wonder how much heavier a nine inch would be compared to the BW?
It's not just the unsprung weight either, a 9" costs you a few extra horsepower to turn compared to smaller diffs too, not a problem if you're rocking big cubes and/or forced induction, but behind a stock 173 you'll loose about half your horses just turning the diff!
Of course that comes back to your budget as well, for a 9" you can get lightened gear sets, roller bearings, gun-drilled axles, etc., which make a big difference but come at a premium cost too.
Also as above, it all depends on how much power you're making and where you're making it, and how much the car weighs, and the size of your tyres, and how much traction they have, and what your intended use is, etc., etc.
Even the gearing makes a difference, lower gears tend to be easier on the rest of the driveline but you have to balance that with the additional RPM, if you're using an old school trans without overdrive(s) it will be screaming it's tits off at highway speeds.
Everything is a trade-off!
But seriously, that is really over-thinking everything, as MAZ said already, pick yourself up a second-hand 9", bolt it in and you should never have to worry about it again (except maybe changing ratios if you want to play games on the quarter mile later on), just make sure you buy one that suits the UC as they're not interchangeable with the LH/LX.