I have come to the conclusion that the Federation Fleet at Voyager; Endgame must be roughly 20 to 25,000 active Starfleet Starships. Voyager's Registry # is NCC74656. The first Enterprise under Archer was/is NX01 and the USS Enterprise under Kirk was/is 1701. So obviously, the UFP being about 150 years old by the end of Voyager, Season 7, would have had to produce around 70,000 ships.
Now between ships being de-commissioned, scrapped, and destroyed over that period, and with continued construction and refits, the fleet would fluctuate to this amount. Remember, Runabouts and Peregrine Fighters are numbered also. The Rio Grande had a registry number NCC72452. Their small size and necessity for a small craft with easy construction would account for around 5,000. Other fighters, another 5,000.
Now back to the Primary fleet. Starship fleet. Given the vast area of Federation Space, the size and amount of Starbases and such, they would have only been constructed to facilitate a large fleet of thousands of ships. Despite the battle of Wolf 359 and the dialogue of TNG, there is just no way it would consist of a few hundred or even a few thousand. At the end of 'Best of Both Worlds' Commander Shelby stated that the fleet would be up in a year. But "the Fleet" can be a subjective term. The fact that JUST one ship (A Borg Cube) could destroy 38 Federation Starships made it seem like a bigger deal than it was. In DS9, there were constant examples given that Starfleet was much larger. And the Klingon Fleet was almost as large. Together they would have surpassed the Romulan Fleet, but not separately.
Remember, the Romulan Star Empire was the Dominant superpower throughout TNG. In DS9 during the Dominion War, it took all 3, to challenge the Dominion's Alpha Quadrant fleets plus the Cardassians, and then the Breen fleets. The Cardassians were threatened by the UFP and in DS9, beaten quickly by just the KDF. During the war, when the Dominion got a hold of DS9, The Dominion, was almost able to get in another 3800 ships when the cloaked minefield was taken down. That would have "sealed the deal" in winning the war. Obviously that's not all of the Dominion's fleet, but around 1/8th (est.). Their fleet would most likely be close to 30,000 total.
The Romulan Fleet, 25,000 with much of it being the large D'deridex Class Warbird. They had the Reman Slaves to manpower such large construction efforts, unlike the UFP. Clearly Starfleets' bulk is the Miranda Class, the Excelsior Class and the Nebula Class. Followed by the Galaxy Class and Akira ships. They would have had to double their efforts building and housing larger ships to combat possible Warbirds. More advanced mission focused ships were built on demand. Like the Intrepid, Defiant or Olympic.