There is no evidence that the Terran ships in the mirror universe are any more powerful than those in the Federation. For instance, in "Shattered Mirror" (DS9 S4E20), Sisko is brought over to the mirror universe to help build another version of the Defiant. This Defiant is exactly the same as the prime universe Defiant (indeed, it's built from the specs mirror O'Brien saw on prime DS9); however, the Defiant is still a major player in the battle, and it seems that the Defiant is still matched evenly with the Alliance's ships. This would not be the case, however, if the mirror universe ships were substantially more powerful.
Another piece of (circumstantial) evidence I can think of the (other) Defiant seen in the two-part Enterprise episode "In a Mirror, Darkly". This Defiant, crossing over from the prime universe, is used by mirror Hoshi Sato to very quickly take over the mirror version of Starfleet, and I suspect this would not be possible if the other mirror ships were heavily armed and able to put up a fight against the Defiant (which is not from that far into the future of the prime universe).
Clearly, war and conquest is a major focus in the mirror universe, so one can only speculate as to why the weapons are not more powerful - my personal guess is that with the perpetual war-footing that everyone found themselves in, science and engineering took a permanent backseat, and so weapon technology did not progress as quickly as could've been possible.