Fitzsimmons is cleary one of the greatest p4p in terms of resume but I don't see anything on film that would make me favor him to beat Hagler.
I'm a massive appreciator of what Fitzsimmons accomplished. The guy was a physical phenom with one of the weirdest frames I've ever seen. He was also tough as nails, hit like a freight train and was an utter genius. However, I firmly believe his style would look extremely odd in the modern game, as newer, thumbed, bigger gloves lead to different fundamentals being necessary for subsequent eras. Massive parts of his game would be lost. His usual parrying and milling wouldn't work; nor would his wrestling and infighting. Since weight/dates aren't named, I'll assume it's one Fitzsimmons' fights between the Mayer fight and the Hall rematch - which is what I'd consider Fitz' prime/'middleweight' peak. However, even in this version, I don't think he'd beat Hagler. Hagler was a master boxer-puncher with a titanium chin and all the technical skills a fighter could want. He was also cold blooded when he wanted and I think here, he'd fight how he did Hearns and really batter and ware down Fitz. There's also the fact that you're picking between two all-time greats, and you have to guess how good one of them was. We know how good Hagler was, and that familiarity makes him a more sensible pick IMO. Although, picking Fitz isn't too out there.