For convention photography, the 24-70mm f/2.8L II is the better choice of these two. In tight spaces, the wider focal lengths are much more usable, while a 70-200mm often requires you to stand farther back than the venue allows. It also helps in low light, since shorter focal lengths are easier to hand-hold sharply at slower shutter speeds than longer telephoto shots.

The 70-200mm can still be excellent for portraits and more compressed “beauty shot” looks, but it’s less practical on a crowded convention floor. Several users also noted that the 24-70mm is extremely sharp and more versatile overall for this type of event work.

That said, neither zoom is especially fast for very dim light. If low-light performance is your top priority, a fast prime may be worth considering, since it can give you at least about a stop more light, though you give up zoom flexibility. A prime can also be lighter to carry all day.

Bottom line: for conventions, get the 24-70mm; for dedicated portrait/beauty work, the 70-200mm has advantages; for the darkest conditions, consider a fast prime.