I'm sure the Federation would field some larger ships in an extended war with the Klingons. I just don't think they'd look exactly like the ships the Federation produced in peacetime with exploration in mind. Since the war timeline does have a ship that looks exactly the same, it must indicate something about the similarities of the timelines.
At any rate, I still find it hard to believe that, in a prolonged war with the Klingons, Picard, Riker and the others all ended up in the exact same positions on the exact same ship. Again, that their career paths converged so exactly must say something about the similarities between the timelines.
Perhaps the parallels between the timelines say that the Federation didn't take the war as seriously as it should have in the early stages, so they focused just as much on exploration as they did in the prime timeline, but Starfleet found itself ground down by the relentless Klingon advances until they realized they should have been putting more resources towards the war then had been. By then it was too late....
To be technical, the E-D didn't look exactly the same on the bridge, and there were subtle differences on the interior shots. While it probably was mostly due to the cost of modifying the ship models for just a single episode, one can infer that maybe there were subtle differences to the exterior we could not see (IE enhanced shields, phaser arrays, torpedo bays we could not see, and the like). We just don't know.
I get what you are saying about how the timelines are too conveniently similar, but if you want to avoid tedious discussions, this
is one to avoid, LOL!
The thing about alternate timeline and alternate\mirror universe episodes that have if you think too deeply about it, there shouldn't be the same characters at all. One event could erase cities of people. Butterfly effect and all that.
But yes, it is a fair assumption that both Federation and Klingon ships are close enough to the prime timeline to calculate a possible winner. But, it also must be considered when the war started, as well. 2340s vs 2372 is a big variable to account for, so in a word, all bets are off if you are strictly going by the YE timeline to say the Klingons would absolutely win.
BTW, like I said earlier, think it would be a stalemate for both sides, or Pyrrhic victory for the Klingons. I don't think the Feds could decisively defeat the Klingons.