Another thing to point out is how the strength of a Galaxy's hull. I noticed in the alternate history shown in Yesterday's Enterprise that without shields, the Enterprise seemed to remain intact despite numerous disruptor shots. Although we saw this in an alternate universe, seeing as the Galaxy didn't seem extremely different, I would assume that the prime universe Galaxy could withstand disruptor shots with shields down.
I agree. It seemed the primary difference with the Galaxy-class in "Yesterday's Enterprise" was its mission profile, with a higher priority towards tactical operations, and less civilians around. I suspect that the Galaxy-class ships that participated in the Dominion War were probably the same.