It depends on the kind of 'M and Missingno and of course the level of both, their stat experience and moves. I assume you mean 'M (00). If so:
If it is a battle between 'M (00) and normal Missingno. in Red/Blue, the one who uses Sky Attack first would probably win, like camper says.
If 'special' Missingno. (B6, B7, or B8) counts, it can copy the base stats of other Pokémon (the last in the party other than another Missingno. of the same kind, or the last Pokémon in battle), as well as the starting moves and TM/HM learnset, so if it copied something like Mewtwo it could easily win against an 'M of the same level with a damaging move, because 'M (00)'s base stats are very low in terms of HP, Defense, Special and Speed.
Note Missingno. can learn different moves through the Johto guard glitch. For example, Missingno. (89h) can be obtained via the Johto guard glitch with Smeargle, allowing it to learn most Generation I moves. If Missingno. (89h) used something like Spore or Thunder Wave, it might have an advantage.
If it was a battle between 'M (FF) (aka Charizard 'M) and R/B Missingno. Its speed and decent enough Attack/Special would allow it to have an advantage and probably beat normal Missingno. with one hit because of its low defenses.
If there was a battle between 'M (FE) (that evolves from ゥ (E3)
at level 255) and R/B Missingno. it would be closer because it has Slowpoke's base stats which has better defenses and speed.
If Yellow Missingno. is taken into account, its massive HP would give it an advantage against 'M (00) in an inter-game link battle but I don't know if it would win. 'M (FF) would probably beat it.