There are exceptions, but, generally speaking, bulk ferments are a Neapolitan thing, while balled ferments are NY.
Atticus, you should never split the dough after the 'final' ferment. Bulk ferments are always part of a two stage process. Bulk, ball, then a secondary ferment. If you bulk, ball, then form, the dough will not have had a chance to relax and it will be incredibly difficult to stretch.
Fermentation generates heat, which, in turn, accelerates fermentation. In a big chunk of dough, the center is insulated from the outside, so it will have a tendency to get warmer and ferment faster. You can compensate for this, to an extent, by starting off with colder water/colder dough. The biggest advantage of bulk ferments, by far, is space. In a restaurant where space is a premium, bulk dough takes up a lot less space than balled dough.
Cold fermenting bulk dough doesn't really work, imo. When Neapolitans bulk ferment, it's always room temp. Bulk dough takes forever to chill and forever to warm up to a sufficient temp so you can ball it. You don't want to ball cold dough because the coldness will make the gluten tight and more easily torn. The long cool down, the long warm up, the (generally) overnight cold ferment, the post balling minimum 6 hour room temp ferment to allow the dough to relax- it all adds up. Sure, you can start off with ice water, so the cool down is quicker, but you're still talking about extra steps, extra hassle and, imo, greater room for error. I also believe that cold bulk fermentation introduces the potential for widely varying levels of fermentation in the dough mass (depending on how large it is). Mix, knead, ball, cold ferment, warm up, form- much more simple, and, imo, much more flexible, as long as you have the space. In order to achieve the best pizza possible, pizzeria architects really need to think a bit more like bakery architects and include additional proofing space (preferably refrigerated) in their designs.