It's not remotely close. Ali-Frazier was two icons of their time in three terrific battles (well, two terrific and one pretty good one) whereas the Holyfield-Bowe series featured two good heavyweights. They were just fights. Ali-Frazier things were events.
Ali-Frazier was more meaningful in boxing history I feel. I do think that bowe-holy produced a better series of fights though.
Certainly Ali-Frazier, bookended by the FOTC and Manila epics. They were transformational events which matched the hype. Ali made Frazier rich, and Joe proved Muhammad great. Frazier's passing was a headline event, even in 2011. Together, they helped revive boxing, a struggling sport until they undertook their rivalry. Ali hyped and hyped them, continually building up anticipation for each of their matches, even between their bouts while matching other opponents. If Frazier had somehow defeated Foreman in their rematch, Ali-Frazier IV would have been another monstrous event (although this time somewhat anticlimactic with Joe's continued physical decline combined with Muhammad's optimal training sure to be undertaken after the experience in Manila). While Bowe and Holyfield had a fine trilogy, I don't think the potential was there to promote it into a quartet of bouts. It seemed clear after their third bout that their series was concluded (although both were still young enough and viable enough to offer promise of a fourth match). Even during the post fight conference after Manila though, Joe was promising that each time he squared off with the Butterfly in the future, they'd provide an excellent contest, and Ali was adamant that Frazier should definitely NOT retire after Manila. The wheels in both their heads were turning over the prospect of yet another bout between them in the aftermath of their third classic. Ali-Frazier II on it's own, separated from the context of the FOTC and Manila, is actually an excellent heavyweight bout, perfectly suitable for the 15 round limit (like Ali-Mac Foster, and Ali-Bonavena). Ali-Frazier II was actually Ali's peak of preparedness and conditioning for their series, although the chip was off Joe's shoulder after the FOTC, and his World Title gone. Bowe seemed to decline somehow after each match with Holyfield, and their rivalry is really the only thing for him to hang his hat on historically. I'm not sold on him as a legitimate IBHOFer, regardless of whether or not he ever gets inducted, one of the few undisputed HW champions to not belong in there who remain excluded (along with Leon Spinks and Buster Douglas-I think Carnera's brief but active title run with two legitimate wins over HOFers Sharkey and Loughran entitles him to finally be enshrined, by the IBHOF's admittedly diluted standards). Despite Bowe's 43-1 record, I don't believe he truly proved himself to be an ATG, only as having ATG potential (like a properly trained and motivated Douglas). Peak Frazier is a top five ATG HW to many, and Ali's common acronym is the GOAT. Boxing was revived by Ali-Frazier, while Bowe-Holyfield failed to reverse boxing's decline from mainstream prominence. Bowe's actions after their first bout also guaranteed that their subsequent bouts could not be for all the marbles (although their subsequent rivalry did overshadow that).
Ali-Frazier as a series, though the first Bowe-Holyfield fight is my favorite heavyweight contest of all time.
Ali-Frazier if I could only watch one, however if i was going to watch either trilogy right now, it would probably Bowe-Holyfield.
Holyfield-Bowe is the better trilogy imo Frazier & Ali were made for each other but the clash of styles between Holy & Bowe is even better. An undersized but ferocious warrior vs a big badass, though it lacked the high-profile personality clash between Ali & Joe their fights were just as dramatic. FOTC & Manilla are legendary epics but their 2nd fight wasn't that special, all 3 Holy-Bowe fights were great :yep
Ali-Frazier and its not that close. Ali-Frazier produced the two best fights in HW history and their second fight was pretty good too. They were also better fighters than Bowe or Holyfield.