D.W. Griffith could have made any film he wanted to after the enormous financial success of 'The Birth of a Nation'; he chose to make the most technically ambitious film to that date, 'Intolerance.' He took a risk with such innovations in film montage and form, and the well-known financial train wreck resulted. Buster Keaton doesn't take that kind of a risk with 'Three Ages,' a parody of 'Intolerance.' This is Keaton's first feature-length film of his own (he only acted in 'The Saphead'). He had the fallback plan of dividing the three episodes in this film into three separate shorts, which Griffith did do with 'Intolerance.' Keaton didn't have to. Chaplin had already succeeded with feature-length comedies, so if Keaton was taking a risk here, it was completely calculated.
Chaplin had already done a parody of another film, too, with 'Burlesque on Carmen' (1915). Keaton appears to allude to that film, as well. The wrestling scene in the Ancient Rome episode references the swordfight that turns into a wrestling match in Chaplin's film. The comical distance from the plot of both scenes is the same, too. Furthermore, Chaplin's film imitated the glossy style of DeMille's 'Carmen,' and Chaplin's film seemed a tribute to that film. Keaton doesn't attempt the radical editing, narrative structure or monumental nature in his parody, but it seems respectful of 'Intolerance' nonetheless. At least, the stories aren't told completely straightforward as in other post-'Intolerance' films, such as Dreyer's 'Leaves from Satan's Book' (Blade af Satans bog, 1921) and Fritz Lang's 'Destiny' (Der Müde Tod, 1921). There is some mild jumping back and forth between episodes.
Where Keaton did take risks, however, is in his physical, daredevil comedy. That's Keaton unintentionally failing to jump across buildings in the modern episode. Reportedly, he was convinced to alter the scene rather than attempt the jump again. And, it wasn't just Keaton who took risks; the anachronistic baseball gag, for example, was rather dangerous. Thus, although in a different way, Keaton, like Griffith, took risks with his big film. And, I think they both succeeded.