Something of note is that, however strange the coincidence may be, in both the MOTHER series and the Chrono series, you fight all-powerful Lovecraftian rejects, and at some point in both series, you have to defeat those creatures with a song. So I imagine that, at least mechanically, Crono probably couldn't beat Giygas, but in a funny way, Serge, who is widely regarded by many as his inferior, would have the means to do so, what with the Chrono Cross being a few musical notes, albeit ones of great power.