I think I'll begin with some assumptions. A type X phaser (galaxy class standard) does 100 damage per second. All other weapons will be based on that number.
In a Galaxy vs. Galaxy engagement with only phasers, it should take about 60 seconds of pounding before the forward shields are taken down (maybe 30 seconds with a photon torpedos). Throwing in maneuvers, hitting different shields, and other unknowns of battle, the actual engagement would take several minutes. But 60 seconds of pounding with a type X phaser for a Galaxy class's forward shields to go down is another assumption I'll make.
Galaxy class ships don't really shoot their phasers for very long stretches of time. Maybe 3 seconds out of every 10.
So that means that out of the 60 second engagement, there are 18 seconds of total phaser fire. 100 damage/second means that a Galaxy class's forward shields will be 1800 units. Galaxy class ships are cool, so we'll make it an even 2000 units of shields.
Everyone knows that starships can take a lot of punishment after shields are lost. Starfleet ships generally don't really have much armor to speak of, but their outer hulls HAVE been reinforced against weapons and other badness. So we'll assume that the Galaxy can take another good smack with phaser fire before internal structure starts to erode. 300 units of armor
Internal structure is going to last at least as long as the shields did before the ship becomes lost. We all know how often the Enterprise loses shields, but keeps on fighting through the commercial break. I'm inclined to give it the same value as the shields (2000). That may seem like a lot, but remember that there is only one ship hull, but six shields (well... actually 8 right now, but we'll talk about all that some other time). So shields are 6 (or
times as powerful as internal structure.So it'll take 60 + 10 + 60 = 130 seconds for one Galaxy to destroy another with no maneuvering, or photon torps. If torps are 50% of the damage dealt by a Galaxy, then that would make it 75 seconds.
75 seconds is the minimum time. If the target ship maneuvers a bunch, and spreads the damage across all 6 shields, then it would take 30 + 30 + 30 + 30 + 30 + 30 + 5 + 30 = 215 seconds, which is almost 4 minutes. Assuming that it'll average out to halfway in between, that's a 140 second engagement from start to finish, 2 minutes and twenty seconds.
I'd say that's about right for a one-on-one duel. Faster paced action will happen in larger engagements, when multiple ships can concentrate their firepower.
