Ah, I got the wrong impression about the movie, which I have never seen, sorry to say... A Buckley
wouldn't be quite as overwhelming an opponent to the sub as a full destroyer in terms of speed and gun firepower. That is, Kirk firing phasers at the distant Romulans when their cloak flutters would be analogous to a situation where a stable and speeding destroyer would be firing the 4.7in guns at a briefly surfaced sub - a fireworks display quite different from a badly rolling DE firing her 3in guns or Hedgehogs.
But as said, FASA gameplaying sometimes involves a Bird of Prey opponent that is a fairly even match to the Federation heavy cruiser, essentially a #3. In firepower terms, that is.