To my knowledge, Marilyn was never in a catfight in a movie or, for that matter, a publicized real life scrap. However, it has been written that she was a toughie having spent some time in an orphanage and several foster homes. Bettie Page also had a tough life as well. She was arrested in 1972 for assault and battery on her husband. She was 49 at the time and, according to reports, was punching and verbally abusing her husband when they arrived. So, I guess that she had a certain level of aggressiveness.
I did a little research. Both ladies were about the same height with Marilyn being 5'5 1/2" and Bettie being 5'5". Marilyn measurements were listed as 36-23-37 while Bettie's measurements were listed as 36-22-35. In their prime, they each weighted 118-120#. although their weight did fluctuate as high as 128#. over time. Depending on the source, each lady wore either a 34B or 34C bra. Review of topless pictures would suggest that a 34B was probably more accurate.
This would have been a great matchup for a Catfight given the similarity of size. My guess is that Bettie would have edged out a victory in a long drawn out donnybrook.