The Klingon BoP
does look very Klingon. Exactly how beyond name and wings is it Romulan?
Some examples that come to mind:
Romulan Bird of Prey was mono-hulled, utilizing a saucer. The Klingon BoP was dual hulled, with a configuration similar to the Klingon Battlecruiser. The front hull was at the end of a thin neck with a round head at the tip, and a round mouth-like weapons port mouth. The Romulan BoP's weapons port wasn't a recessed mouth like that at all, despite being in the
center front of the saucer.
The Romulans had up-swept, soaring wings, not mostly downswept aggressive ones like the Klingons. Rarely are the KBoPs wings up.
That they both use bird motifs is not unusual as birds and flight have universal appeal among human cultures as well (look at national flags or crests or religions (angels) or mythologies (Pegasus)). Cardassians and others like birds too. We all have wing-envy.
That the KBoP came after a theoretical alliance between the two powers also suggests it's kosher. Romulans had no problem using Klingon ships in TOS ("The Enterprise Incident"). Influences between cultures is common enough; interestingly, I think one of the designers of the Vor'cha said you could see on it some Federation influences as well.
That Romulans continued their bird design dominance with the warbird matters little as its introduction in the real world on TNG came years after ST:III had already introduced the KBoP. Also note in-universe, if you must, the use of a winged Raptor ship in ENT, as well as earlier KBoP's and the similar looking D-5 (which shouldn't look that way for other reasons, but there it is).
The KBoP has giant weapons at the end of the wings. Although both Klingon and Romulan ships of TOS had nacelles, the guns suggest aggressive Klingons (esp of the recent TOS movies) more than the graceful Romulans or yore.
The KBoP is a crusty, gnarled, K't'inga-like over-detailed, rust bucket. Whereas the RBoP was a slick Raygun Gothic design out of Flash Gordon. The warbird also has a very much more organic design to it than do the greebly K't'inga/KBoP.
There are others as well.
The matter gets further confused when you notice how little has remained of the RBoP's look in later ships. The D'deridex "Warbird" has a head, like the K Bird of Prey, and the Valdore Warbird looks less like a triple-hulled Warbird than a giant en-Romulan-ified KBoP. To me, this speaks to a dearth of creativity in Trek during the waning years of the Berman era. ...I mean, we got the Valdore and the Space-Nosferatu Remans in the same movie...