I imagine the Klingon empire is larger than the Romulan empire, but that's based more on the fact that the Klingons were more of a match to the Federation, whereas the Romulans, though dangerous, were isolated from the rest of the galaxy by the neutral zone. Besides, what does "size" mean? Population or just controlled planets? Or maybe just the size of the military counts?
Earth and her allies fought the Romulans in the 22nd century, before the development of the Federation. I don't know that the Federation ever had a shooting war with the Klingons in the prime timeline. They had a cold war akin to the US-USSR tensions, for sure. The Organians put a stop to the shooting, but they were motivated more by the annoyance of the activity in their system, I think. If the Feds and the Klingons wanted to fight somewhere else, I'd not expect the Organians to stop it again. Though just because the Organian Peace Treaty is not mentioned again after TOS, there's no reason to think it didn't remain in force.