I'm sure people already listed a bunch of reasons why either character would win, but here's why I think Hyper Sonic would win. Sonic doesn't go into his Super Form unless going up against a real serious threat, much less his Hyper Form, so already I think he's gonna try going for a one-shot here. However, my real reasons for Hyper Sonic winning is that even with speed equalized, Sonic still has a 8x speed multiplier thanks to his boost, and thanks to recent changes to Sonic's verse, Sonic's BFR thanks to Chaos Control should be 5-D, possibly 6-D (unless restricting Hyper Sonic to 2-A keeps that from happening). Aside from that, Sonic has experience fighting reality warpers and time controlling enemies, and he has quite a few resistances to corruption, mind manipulation, dream manipulation, and other haxes that Bill might use. Frankly, I think Sonic (if he were already Hyper) wouldn't hold back at all and would either deal enough damage fast enough that Bill regen wouldn't work (it does take some time) or would use the Chaos Emeralds in some way to overpower Bill.
So yeah, Sonic FRA