I think we've had a few of these threads before. The Mega Evolutions are lacking in lore, so post your headcanons here.

Upon Mega Evolving into Mega Mewtwo X, Mewtwo's physical strength increases greatly. While its psionic capabilities haven't improved, it can now tap into its vast intelligence to deliver its physical blows with perfectly calculated strength and precision, drawing from (and building on) its knowledge of various human martial arts.

Mega Mewtwo Y isn't a lame speed form for a shitty female Mewtwo, but rather the form that Mewtwo attains after the Mewtwonite Y converts most of its mass than brainpower. Its intelligence and psionic capabilities have increased greatly due to its enormous head, but this sudden enlarging of its cranium has also made it mentally unstable. Mewtwo has now reverted to a childlike mentality, unable to experience any emotions other than the constant rage and pain it felt as it was growing up in Dr. Fuji's lab, and is far more vicious and unstable in this form, constantly throwing what can be best described as superpowered tantrums, often allowing its anger to overcome its sense of reasoning.