Different timeline, but the same resources. Both Starfleet and the KDF were fielding the same ships in battle. Three of the big BOPs were a match for a Galaxy.
Not the same resources. The conflict started in 2346, or there abouts. Up to that point, Starfleet hadn't seen a lot of ongoing combat for a while, AFAWK. They weren't set up for a big conflict at all. While Klingons are basicly always prepared for a big conflict, it's part of their culture.
In 2372, things are different for Starfleet. They encountered the Borg, and the Dominion, and realized just how seriously underpowered they were. Thing started to change, ships like the Defiant and Prometheus were designed, they came up with pulse phasers and quantum torpedoes. So yeah, they stand a much better change against the Klingons then they would in 2346.