The sense I always got was that the Warbirds' technology were overall inferior to the Federation's, especially with Galaxy class and newer, and the only thing that might give the Romulans the edge is cloaking technology.
I didn't get that impression at all. If anything, TNG attempted to portray their technological level as essentially the same. Unlike all other powers, where the rival was shown to be weaker (this includes Klingons and certainly includes Ferengi and Cardassians).
The Romulans must fear the Federation's strength for some reason though, otherwise they wouldn't demand by treaty that the Federation not be allowed to have a cloaking device.
Well, no one knows what else was in the Treaty of Algeron. It redefined the Neutral Zone and it prevented the Federation from using cloaking devices. Roddenberry said that cloaks were antithetical to the federation, so they might not have seen it as a huge loss. The Romulans don't want the Federation using cloaks because it helps them preserve an advantage. The Romulans can go freely into the Neutral Zone, the Federation generally stays to their side. There's no reason to think the anti-cloaking provision was out of fear rather than just preserving an advantage.
There's not enough evidence one way or the other to say. Tin Man seems to be the episode that considered technical capacity the most. It makes clear that the Enterprise is faster than a Romulan Warbird. On the other hand, Romulan disruptors seemed effective at incapacitating the Enterprise even with shields. Romulan shield capacity wasn't tested (I can't think of an episode where a Galaxy class fired on a Romulan Warbird). Overall, probably not enough to go on. I think it's fair to say they can both destroy each other (hence the whole Balance of Terror, Mutually Assured Destruction themes).