YEah, the Galaxy class was still very new when the Sovereign class went into service. The Galaxy class is heavily armed. I remember there was always people in the show making a big deal in Ds9 especially when something had more fire power than a galaxy class starship.
The Phaser Arrays on 24th century vessels take from a single power source unlike the weapons in the 23rd century that used phaser BANKS. Each beam in the 24th cenutry has several times more power pouring through them than the dual beams of 23rd century vessels. (However it would seem they went back to some sort of seperate power cells for the pulse phaser turrets of the Defiant).