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http://media.comicvine.com/uploads/0/1494/87382-14271-bat-mite_large.GIF

vs

http://media.comicvine.com/uploads/9/95856/1983543-x_men_legacy248_0009_large.jpg

Exactly how powerful is Legion? Bat-Mite is still a 5th dimensional imp. And even if he's not as powerful as Mxy, well, he's still insanely powerful. I know the fight they had in that WORLD'S FUNNEST thing was an ELSEWORLDS, but if that's any indication of how powerful Bat-Mite is compared to Mxy, he's still on a universal level.

Spite

BigTime spite. Bat-Mite wins

Legion Wins.

An in character Bat Mite wouldn't try to kill Legion but rather would likely try to play games with/play tricks on Legion. Eventually, Bat Mite becomes bored and self BFRs, giving the win to Legion.