The advantage is you may be able to lock in a really good room, especially if they've pre-upgraded you to a higher room class. A related advantage is, if you're arriving late, you can prevent being assigned the dregs, which is particularly important at hotels which do not pre-block room assignments. There's a thread on this, and the general consensus is you need to make a judgment call whether you're likely to do better with the mobile room selection or at the front desk.

Hilton is IME the only chain where mobile check-in can in fact provide a meaningful benefit.