Either way, it doesn't necessarily mean that it's shields are far superior to that of Galaxy or Nebula, it means that they recharge quicker, but since Galaxy/Nebula are so massive, their raw shield power output has to be greater than Sovereign's. In Star Trek, bigger is always better.
Indeed? I think one of the lessons of the Dominion War is that capships are intensely vulnerable to swarmers that manage to get inside the gaps in the capships' firing arcs. I hope the first thing they corrected on Sovereigns, Akiras, and later vessels was the lack of close-in capability that could dissuade Jem'Hadar fighters from exploiting the gaps in Galaxies' and especially Excelsiors' phaser batteries.
As a small aside, imagine the problems a Constitution would have had with a flight of Jem'Hadar fighters. That thing was made exclusively for standoff fighting. With less than a third of approaches angles even covered by weapons, it looks like the Rodney compared to the Galaxy's Yamato.
But for some reason, in the Dominion War as depicted on DS9, everyone frequently decided that they'd arrange into "lines" in three-dimensional space and wait around at sublight for the enemies to come try and "break through the lines," which they inexplicably did by also dropping to sublight, flying in tight formation with one another and moving to extremely close range with all the Dominion ships.
We have to give 'em a bit of room for artistic license I think.
TNG often rattled off distances of thousands or tens of thousands of kilometers between combatants in small-fleet and ship v. ship actions, but on-camera evidence contradicted this heavily. Other than the swarmers (Peregrines, Defiants, Mirandas/Soyuzes/Centaurs, Jem'Hadar fighters, BoPs) I think it might be better to assume that the battlelines formed larger fronts than shown. I know it doesn't show on the screen, but the alternative is assuming that both Fed and Dom combatants are too stupid to go around a concentration of ships taking up no more than a thousand cubic kilometers.
As for dropping into sublight, I also think that's attributable to the warp-breaking technology demonstrated in BoBW. It's definitely possible in the Trek world to force a ship from warp, by creating an warp field inimical to the adversary's propulsive field. Hey, if it worked against the Borg, I'm sure it work against the Dominion.
So it's probably preferable to assume that the "lines" are square formations millions of kilometers wide and tall that, after an appreciable fraction of an enemy fleet has been forced out of warp, concentrate. Both sides jockey for a superior position, like World War I battlelines. Somehow they tend to wind up facing off rather two-dimensionally. For the Dominion, whose doctrine tends to focus on large, expendable swamer fleets, kamikaze attacks and particle beam weapons over standoff capship battle and photon torpedo contests, closer is probably better.
Then again we see huge Dominion battlecruisers. They seem even more vulnerable to swarm attacks than Galaxies.