The point is the war timeline isn't different, as shown by the completely same people serving in the same ship, which makes it a viable point in arguing the Klingons would beat the Federation, since they did beat them. If the E-D is the same, how could everything else be radically different? It can't.
But it has been established there ARE differences in crew membership
You can't say the Enterprise is the same because you don't know that. There are visual internal differences. All you can say is that the external view looks the same, visually.
While I agree with you that the Feds probably would at best stalemate the Klingons, whom I believe could possibly win (though they would be devastated too), YE is only a possible scenario. Not to mention, in the YE timeline, the war starts some 30 years prior, with the war coming to a conclusion in the 2360s. In the Prime timeline, it didn't start until 2372. A lot can happen in 30 years. It would be like saying because the British fleet could beat the US fleet in 1925, that it therefore should also be able to beat the US fleet in 1955.