With the size of the respective Empires, Klingons are certainly more visible in Star Trek, and but heads with the Federation more over contested planets so based on that they are probably bigger.
That said The Romulans of the TOS era are not quite as isolationist as suggested, The Romulan Commander speaks of hundreds of campaigns of war, asking why it must always be so, and notes the sucess of the prototype will lead to another war.
FWIW the Romulan Admiral in Enterprise notes that he was broken for questioning the Romulan policy of expansion.
It really seems impossible to pin down the total number of planets, anymore than you can for the Federation.
Listing the worlds known is possible though
of the top of my head -
Klingons have Qo' nos, Rura Penthe, Khitomer, Narenda III,
Romulans Romulus and Remus ( and thats all I can think off!)
Well, the Romulan Commander never said they won those campaigns I guess ....
The Romulan war was definitely first, occuring over a century before the TOS era, Humanity did meet the Klingons first though as seen in Enterrprise.
As mentioned its unknown whether there was a full scale war with the Klingons, at least prior to the brief one in Errand of Mercy, though we know there was a skirmish at Donatu V some 23 years before Trouble with Tribbles.
The Organian peace treaty seems to last, at least technically through to ST6 as noted, however Kruge has no real quarms about attacking the Grissom in ST3 ( and the Klingon ambassador, does not disavow these actions as unsanctioned). The Klingon Ambassador goes to threaten " No peace while Kirk lives " in ST4 and a faction of both Klingons and Starfleet are gearing up for war in ST6 so it seems that no one takes Organian enforcement of the treaty to seriously for whatever reason. Then again, the Organians seemed to know that the Federation and Klingons would become allies one day, so possibly they knew how things would unfold all along and saw no need to get involved ( also makes Kirks disbelief at Ayebournes statement a tad more ironic FWIW).