Melodically, they're nearly identical, with the biggest difference being that Mewtwo's battle theme is a half step lower than Mew's. Mew's Emerald battle theme also never loops back to the A section, instead going back to the B section, unlike Mewtwo's FRLG battle theme, which goes back to the A section. The only other major difference is that Mew's battle theme contains an ornamentation towards the end of the B section that isn't in Mewtwo's. Leading up to measure 19 of Mewtwo's battle theme, there's a walk up that ends on a high note on beat one of measure 19, which is held for two measures and is then lowered by a half step, which is also held for two measures. In Mew's battle theme, however, the walk up to the high note is followed by a small ornamentation, with the high note landing on the "and" of two, being held for the rest of the measure, then turning into a hemiola arpeggio figure before going down a half step, being held for a measure, and entering a fast arpeggiated E major 7 lick. Difference shown below, with Mewtwo's theme transcribed a half-step up so they're in the same key.
Other differences I noticed are relatively minor. The C section includes the same countermelody in both themes, though, in Mew's, it's just barely audible, while it's considerably more so in Mewtwo's. The C section also, in both, includes a ride cymbal bell hit on the second and fourth beat of each bar, though it's panned to the right in Mew's theme and to the left in Mewtwo's theme.
