"looking" like it has more power isn't usually enough to win a battle, though. Out of the three that I have battled (i.e. I can't judge manafi just yet), celebi has posed me the most problems. OK, it has seven weaknesses, fine. But it has coped with them exceptionally WHENEVER I battle against it. It's movepool may be small in comparison to mew's, but it still gets some extremely rare/useful moves like heal bell, baton pass, leech seed, perish song (well, that's not very useful on a pokemon without trapping moves), RECOVER (URRGH!!!), and theres probably some more. All on one pokemon (and this is one of the very few that can baton pass AND heal bell). So, IMO, celebi is one of the strongest.
But when they are battling against eachother, I'd say that mew would win because of flamethrower. No guarantees, though, because celebi NEVER seems to die (just... DIE!!), and an un-STABed flamethrower shouldn't pose *too* much of a threat to it. And, of course, jirachi could use her nice haxe-ish moves and win by chance (Jirachi used ice punch! Mew is frozen!) .