Now, based on the current numbers of ships (still subject to change) I have noticed a few things that we can make some suppositions about.
1. The DCA was based on a carrier strike force. They lack heavier designs for the most part that can get into a real slugfest. Right now, not adjusting numbers of the Samarkand Class, they are probably a bit short on escorts for their carriers, but have a powerful force projection for aero.
2. The LCN and the FWLN are both positioned as battleship/battlecruiser navies, with powerful anchors to a squadron in the form of the Tharkad and the Atreus Class. Weaker in aero capacity, they probably supplemented with aero carrying dropships.
3. The CC was a cruiser heavy navy; I say this with even their 11 Du Shi Wang and perhaps 2 Black Lions, with lots of destroyers and corvettes as support. Probably again with some dships that were carriers to support, their role sounds like more of a skirmish and patrol navy, and relied a little more on maneuver.
4. The FS navy... is a hodgepodge. However, some strengths would be the ability - while the Robinsons still exist at least - to move their mech regiments around with good support. The New Syrtis class is a powerful carrier, possibly the most powerful carrier of the Successor States of the era. Unfortunately, they didn't have enough of them to cover everywhere. The Davion destroyers and Congress give a powerful escort to either covering the Robinsons or escorting the New Syrtis class. The biggest problem with the Davion navy is the Robinson class, which also would be covering for transport duty, and therefore not be given combat missions for space superiority in a way that other States can do.
A small theory here, by the way, is the continuous FS shortage of transport and dipping into mercantile fleets for transport (an issue that carries through all the way to the 4SW) may be because of their dependence on the Robinson for transport during the 1SW (and perhaps a bit in the 2SW). If there were 60 Robinson Class ships, that's the ability to move 20 mech regiments that were lost after the extinction of warships; a massive loss that would have been felt by the need to replace both transport jumpships AND dropships.