As a potential user (not the author), what jumps out at me about the two is:

OMRN: No lookaround, eager compilation, can output first match

RE#: No submatches, lazy compilation, must accumulate all matches

Both lookaround and submatch extraction are hard problems, but for practical purposes the lack of lazy compilation feels like it would be the most consequential, as it essentially disqualifies the engine from potentially adversarial REs (or I guess not with the state limit, but then it’s questionable if it actually counts as a full RE engine in such an application).