Sovereign-Class starships were replacements for Excelsior-Class ships, they were built as modern versions of that. Sovereigns were also likely to be built in larger numbers than Galaxies. However the debate on power of the two is the whole debate.
The problem here is that the schematics don't show a lot of empty space on a Galaxy, it looks filled up with quarters for staff, support, and civie personnel. In time of prolonged war, they may gut civie stuff out. This would in fact benefit the Galaxy to plant more equipment in. But I find it odd that in Yesterday's Enterprise, the D would have something to this effect done and three K'Vorts were more than a match for the Enterprise. Yes you could argue that it was storytelling. But I do find it too much of a crutch in all cases.
The Sovereign has less total mass, meaning with even equivalent equipment it would be more maneuverable than a Galaxy, TV-show or not. Problem is that doesn't equal advantage. The Galaxy does not need that maneuverability because phasers can generally be fired anywhere and torpedoes have been "seeking" weapons since before ST VI: TUC. However, once shields drop, the Galaxy has more mass to it, meaning more to peal through to destroy. (Should look up Harry S. Plinkett's reviews of the TNG movies BTW). The D's death was lame, agreed.
Torpedoes are a totally different argument, the "Turret" system would not be superior except in pointed delivery, the torpedo delivery would be a bit faster to target, but otherwise there is no advantage other than being quantum torpedoes. As others have said, Galaxies would be refitted with those launchers, photons are outdated.
The only things that stands out still:
1. The make of the hull can outweigh the hull's apparent thickness in effectiveness.
2. Warp Cores are at best, not thoroughly described -- will explain my position.
3. Type XIIs are not described as being specifically better worse, or if they are different at all.
Ceramic armor used today is superior to other, thicker armors, of yesterday. So to me hull thickness is kind of moot. Especially since you can infer that armor is in constant development, making Sovereigns easier to update so hull armor may be better or at least equal, but that is no end-all at all. Easier because less size to build over. New Galaxies, may get that armor, so I don't think this is a valid area for discussion.
Warp Cores were a point I never agreed, ever, that the Galaxy stood on more solid ground. The argument we had before Beta was that thicker equals better. But in current understandings (and the lack of real evidence against this in ST: TNG). Matter and Anti-Matter would be flung together at the highest speeds possible. Colliders today use longer tubes to get that speed up with magnets, that could (maybe not) be the way Starfleet does theirs. Meaning tall should be better. Mini chambers does not mean contained chambers either so that may be misleading too. In final, as far as WARP POWER, the Sovereign gets the edge, that does not equal to total power output as starships have more than one power source. The Warp Core is the primary source but does not mean the Sovereign can put out more power than the Galaxy hands down.
The Type XII phaser array is not described in detail to my knowledge anywhere. As with all technological developments it may be revolutionary or it may be equivalent with smaller components to be more feasible. I concur that a single sustained shot as evidence of most TNG/DS9/VOY shows seems to be more powerful than the multi-beams seen sporadically. But it is not clear if Type XII is better or worse, or compatible with anything else. One may assume a Galaxy would be slated for refit into this type in the 20 yr cycle. The Type XII may use new methods for generating power more advanced. But I do not believe Geordi was mistaken when he said the Sovereign was more advanced at that time. It's hard to say because Technical Manuals are soft-cannon, and the shows are somewhat misleading or at least inconsistent.
A Sovy Vs. Galaxy fight would probably have been close to even in 2373, or else the Enterprise would not have been in that class. In the 25th Century, something else would make the Sovereign look weak if this were realistic. I see no evidence by the way that says a Galaxy is worth two or three Sovereigns, that is speculation. It's not a proper comparison to make. The Sovereign's hand is more specialization and refinement, the Galaxy can be generalized, it was not specialized, nothing is both because then it's a contradiction.
I am a fan of the Sovereign, of TNG Era shows/movies, it is my favorite. The Galaxy-class is actually my least favorite, it looks extremely ugly to me. But the comparison is apples and oranges. They aren't the same "class" or type of cruiser and is unfair to compare. There is not a hard-cannon guide to why one is better. There is plenty of on screen evidence that Galaxies are tough. But Star Trek is story, and all stories have flaws, I forgive the multiple premature deaths of Galaxy-class ships. I honestly think the Sovereign is better at what a Sovereign does, whatever that mission profile is. The Galaxy is that ship out there operating on it's own with a vast number of facilities and good firepower. I do know the Sovereign could not do the Galaxy's job. In war, I'm not so sure the Galaxy would be more than what a flagship is, a central coordinating platform. These are generally large vessels with great firepower in their own right, but they are typically heavily protected by a fleet of support ships too. Even if the Sovereign is weaker, I'd rather serve on it than a Galaxy.
The Enterprise-F is a logical step. It appears to replace the Galaxy, I'm not sure what it's mass is and cannot say if it will be. But CBS pulls the strings and when they say it's better, it will be better. Per the looks, it seems to be intentionally geared to the late TNG period of style for ships. The coloration and elongated proportions is appropriate, if predictable. At least it's new.