I believe, we really shouldn't match characters from 2 diffrent multiverses, because even if eg. comparing only magical beings, magic and energy pretty much always work very differently and effectiveness of powers would be bounded to specific universum either causing/being some anomalies and some features/things don't exist there... but, of course, if you imply both will go "armor" themselves.... (Oh, and if you're just comparing 2 god-like most-powerful representatives of 2 universums, then there should be pat, draw, alliance - especially both characters wouldn't have any single reason not-to-do-so instead of insane life-death-battle..and considering both really bright-minded)
Truly, but I don't know too much about Sonic's abilities - I just know it/he is pretty skillfull hedghog with superspeed of varying ranges... but I know a lot about Bloom, I believe: she keeps on reclaiming her status of the most powerful fairy of the Magical Dimention and seemingly even beyond; while she summon projection of her Dragon, you can be sure it will do trick (it always does, doesn't it?), so infuriating her - being considerably easier - or making her summon it would be going to be big deal for sure; she defeated and probably even overpowered (even if just for a few moments of considerable soaking with the Ultimate Power of Relix - a power stronger than Dragon Flame/Shadow Phoenix/Water Stars, probably not being creation of her powers, as well as an aforementioned dimention) her non-violent-dark opposite + her own counterpart; probably if Sonic's intentions were bad, she could use her Magical Powder to undo and un-merge Sonic from the emeralds (or she would use it "indirectly", because she can have developed better/stronger/more-suited measures/be powerful enough not use just here mere collected Powder); finding some proper magic/counter in her universum is nearly always possible, really; although haven't been used by Winx Club, the Oppositus' power would make Sonic helpless; if fighting in Omega, some ice snake could freeze Sonic solid; if Obsidian would be still existing, Sonic's own strength shall defeat the hedgehog; does Sonic breathe under water? ?; Bloom is seemingly as powerful as some particular nymph, being potentially a might beyond her universe-bound powers and she's got an access to the bases/foundations of her universe (and still going beyond boundaries of her Dimention, not to forget); even Bloom was lucky to get out of Oblivion, which automatically traps, overpowers and send to unconsciousness to make its prisoner dream their worst nightmare and takes most of the memory away; She's the very only of the Club to be confirmed not to lose any of her heap of powers getting taken-away by the Book; Vortex of Flames not only restored her powers, but extended the Dragon Flame before started earning powers out of Dimention of hers; luring Sonic to the Legendarium Worlds should do the trick...; ...and if it would fail, the Infinity Box wouldn't, easily; using magic directly again should bypass eventual immunity (She's already dealed without magic in numerous battles, not to forget); how about trapping Sonic in some magical trap or so-called force-field? {note: if simply running around her bubble{-like}-trap was a way to get rid of this bidding, Trix wouldn't have been helplessly and clumsily tripping-up inside, I'm sure - Icy would "freeze her way out", Stormy would blast it...}; She most probably overpowered her own Wand; Her Special Power to ally with some being(/s) would help in battle too; throwing him out of the time-space also wouldn't fail; back to not-depending on magic, making Sonic literal hell would be easy-peasy for her - especially, if we consider The WoW's Bloom (also, if any portal to the world of nightmares would appear...the last one was modt probably one-way ticket); I wonder how's going to be about her new cosmos-related powers. .; honuorable mention: considering some non-random help, beings who are personally bonded with Bloom could give her boost, there's Sky for occasions like this, Harmonical Overload Convergence created not-possible power, which shattered her non-violent polar opposite...