The federation is meant to be HUGE. So starfleet I always thought must of been pretty big.
Of course. Let me rephrase. In part because of budget, we never saw more than a handful of ships at once in TOS and TNG and the movies. However, the mention of only a handful of ships throughout Trek and right up until that DS9 episode (Sacrifice of Angels) at least gives the impression that the big starships are few and far apart.
Of course, logically since the Romulans, Cardassians, Klingons etc. are military empires, you'd expect them to have large fleets and therefore the Federation to also have large numbers of ships to keep the balance of power.
But 1200+ ships on one side of one battle ? That's like two orders of magnitude bigger than the next biggest battle prior to that.