The Federation might well defeat the Klingons, if they ever had the desire to do it. But they tend to favor diplomacy over combat, and wouldn't even wait to have the Klingons on their knees before trying to talk things over. Whereas the Klingons will go to war full-tilt and won't hold back the way the Federation always does. Even in the short war with the Klingons, how many resources did Starfleet really commit to the conflict? Did the top brass and the politicians really want to go to full-scale war with Klingons while the Dominion was waiting in the wings?
Consider that after fighting Starfleet for a few months, while fighting the Cardassians simultaneously, the Klingons still had enough resources to fight the Dominion for a couple of years, too. They must have some considerable resources for a monolithic empire, then. They managed to do what it took all the combined cultures of the UFP to do!
In the event of a long-term war between the Klingons and the UFP, would the UFP hold together? Or would some species withdraw from the UFP to avoid the wrath of the Klingons? When the Klingons fight the UFP, do they think of all the members equally, or are they targeting just the Humans and the Vulcans?