As Rosalina it can be pretty easy to underestimate Mewtwo. He's a big target and can die pretty early to a good Luma smash or uair, not to mention he is easily outranged with Luma out like most characters.
However, he has some unexpectedly good tools to help deal with the little star, the most unassuming one being uncharged shadow balls. They easily chip away at Luma's health until he can be launched by a safe move like Mewtwo's dtilt, and if Rosalina tries to pull them when Mewtwo is too close he can easily punish with a dash attack, which will also send Luma flying easily. He can also use his down throw to hit Luma if he grabs Rosa with him around.
Due to Rosalina's height, Mewtwo can use short-hopped nairs to good effect against her, not to mention easier surprise shadow claws or dairs.
With Luma around Confusion is hard to use without Luma retaliating, and it is very hard for him to land a Disable since Luma will usually take the hit, and even if he doesn't he can still freely attack while Rosalina is stunned. Without him, the two characters have comparable reach but Mewtwo hits harder with both more powerful moves and better combo ability, attacking Mewtwo following a Confusion becomes very risky leaving jumping away as the best option, and disable can severely punish a whiffed move.
Offstage, it is very difficult to edge guard Mewtwo if the player knows what they're doing since Mewtwo has many options to recover with and evade attacks. Jumping out to meet him at the side will usually result in him teleporting past you, and his big second jump coupled with his good airdodge give him better mixup potential on the ledge than most would have you believe. On the flip side, Mewtwo can go extremely deep to edgeguard and is very good at exploiting the lack of a hitbox on Launch Star with his nair.
Finally, Mewtwo has surprisingly good mobility on both the ground and the air which, coupled with his Confusion jump, good airdodge and teleport, help him avoid engagements with Rosaluma that would normally leave him at a disadvantage. It also helps him reset to neutral more easily.
With defaults this is most likely even since it mostly comes down to who is more patient and makes less mistakes, and Rosalina doesn't really die that much later compared to Mewtwo, especially since she is a slow faller and Mewtwo's best kill moves do it off the top. In customs probably 55-45 for Rosalina since she gains Shooting Star Bit and Luma Warp that Mewtwo has to watch out for, but other than that nothing that drastically changes the game.
