Well after the Tal'Shiar/Obsidian Orders failed attack on the Founder world in DSN, the Founders didn't consider those two Empire's to be a threat to them any longer.
If the Federation is the largest in terms of volume of space (some 8000ly span) that might require a high number of ships to support it. So it is possible in terms of raw strength of ships the Federation is the most powerful.
But a larger area of space can be harder to defend, who knows what other agressive powers are lurking around the Federation large borders?
There were 20 ships in the Tal'Shiar/Obsidian Order attack. So roughly half and half or maybe a 5/15 ratio respectively since the Cardassian Keldon class was smaller. That's hardly going to cripple an entire empire.
So the fleets were manned by renegade intelligence agents mostly. Those two intelligence agencies were definitely crippled for awhile, the Obsidian Order having been said to have "fallen" in Season 4 of DS9 but the Tal'Shiar was a going concern again by season 7.
As for the Federation being 8000 LY across, while this could be true, you could say the USA is 9500 miles across(the distance from Guam to Puerto Rico) but that doesn't quite paint an accurate impression.