The longer you leave dough in balls, the slacker it will tend to get, AOTBE, to the point of making it really easy to get thin spots. I find that my pizza suffers if I go longer than 24 hours in balls.
In terms of "all other things being equal" - there is a distinction that hasn't been considered and wasn't mentioned by Tom L. There is a difference between comparing the rate of fermentation in a large bulk quantity of dough, which can be faster due to the heat generated by the fermentation process, and whether or not dough - either as bulk or in individual balls, is reballed/balled-for-the-first time and thus put back in a round shape after flattening during either bulk or as an initial ball.
Here's what I mean. If you bulk ferment you're also permitting the yeast time to multiply and get started on the fermentation process prior to balling. When you ball after bulk, the dough will already be on its way and so the leavening process will be much quicker when you ball after bulk versus when you ball immediately (there is also a short lag time when the yeast isn't leavening at all). The more rapid rise that occurs when balling after bulk can be much more able to exceed the effect that gravity has on flattening the ball, making the ball more likely to rise vertically rather than flattening (especially if you're working with a higher-hydration dough). If you ball immediately and don't re-ball, the leavening will be slower when the ball is formed since the yeast has not yet had time to multiply and start working. So the ball will be more likely to flatten out.
So, if you're working with smaller quantities of dough, if you compare: a) bulk followed by ball with b) divide/ball and then re-ball later at the same time as you go from bulk to ball in the a procedure, you should get the same result. If you compare: c) bulk followed by ball with d) immediate divide/ball (once only), you may get a flatter ball with d - especially if you're using higher hydrations since gravity will tend to flatten d more since there isn't as much leavening power when you ball to overcome the pull of gravity to flatten the ball in a tray. This assumes, of course, that we're speaking about having the balls in trays that don't prevent the balls from flattening and not in individual bowls where the bowl limits the ability of gravity to flatten the balls.
I think that this corresponds to what you've mentioned about permitting the dough to be in balls longer than 24 hours and is something different from what Tom L. discussed about whether bulk fermentation is different from immediate balling.
