What impresses me most about Mewtwo (and interests me in giving him a shot) is the many different styles he can employ. Swordsman players look at Mewtwo and see a spacing character; Megaman or Rosalina players look at Mewtwo and see a disjointed zoner; Fox players look at Mewtwo and see a bait and punish character; I wouldn't be surprised if Yoshi or Pikachu mains found a mixup character in Mewtwo.
To illustrate this phenomenon, behold Gheb:
Mewtwo looks like a wicked combination of Fox gameplay [huge mobility, lots of raw kill power, good damage output, "glass-canon"] and Ness gameplay [extremely evasive in the air, overwhelmingly strong aerials, kill throw] with a better recovery and one of the best projectiles in the game.
On top of this, he's got the ranged/disjointed footsies of Marth, and Samus' ability to punish mistakes from any range.
As a footsie character, Mewtwo excels and is likely top 10, probably a little worse than Limit Cloud, Little Mac, and Ryu. d-tilt is straight up one of the best grounded moves in the game because it denies the opponent from even playing the footsie game most of the time, and because of it Mewtwo can whiff punish attacks like Mac f-tilt that other characters would have to powershield or shield from a close distance to punish.
up-tilt and to a lesser extent f-tilt serve as great anti-airs, to round out a set of tilts that enable him to use walking spacing over dashes if he wishes (a valuable, underrated asset; many characters who enjoy playing footsies don't have the tilt composition to walk a lot, and walking is more precise than dashing).
d-smash is underutilized and allows Mewtwo to space threatening hitboxes with impunity against some characters.
As a disjointed zoner, Mewtwo is also top of his class. Shadow Ball does all the heavy lifting here just as Charge Shot does for Samus. As middling as Samus might be compared to Rosalina or Cloud, she deserves a lot of respect for her ability to punish you for spacing incorrectly or rolling away from her--fully charged Charge Shot/Shadow Ball is almost as good as Limit Cross Slash for damage, but with much more range.
And imagine if Rosalina could just Shadow Ball you for choosing to retreat from her traps! Incredibly scary.
As a bait and punish character, Mewtwo is pretty underrated. His run-in options are top-class. Dash attack is extremely disjointed and punishes way more actions than it has any right to, and up-smash has a great hitbox and ends lives. Dash grab isn't amazing, but if he does grab you, it can mean your death.
His SHAD is in a league of its own. He can SHAD -> f-air in place, phase forward, or phase backward, all while retaining the ability to dash in with his huge speed at a moment's notice. Airdodging gives him the time he needs to accelerate to his high air speed, which means he can catch you out of your own spacing and punish you.
I have had some doubts about Mewtwo's mixup game, as he doesn't quite have the frame data to do what a character like Pikachu or Villager can do in this regard, but Shadow Ball is such a good move that it opens up the playstyle regardless, and Confusion command grab mixups sweeten the proposition.
If you fully charge Shadow Ball, the opponent is encouraged to play in a way that minimizes the risk of taking a quarter of his stock (or ending the stock), thus opening himself up to getting hit by Mewtwo's other options.
On the other hand, if you don't charge it, you gain mobility options and can use baby Shadow Balls to disrupt options.
This move alone supports the existence of a mixup-oriented Mewtwo, and lest we forget, his n-air would probably be one of the best mixup options in the game on any character, not just Mewtwo.
And no matter which of these styles you pick (though I suspect that the ideal Mewtwo would use a different style in every matchup and even in different situations), he's also got high-tier+ edgeguarding to support it, and two kill throws.
There's such a vast array of positive qualities that recommend Mewtwo. He basically takes the best characteristics of Fox, Ness, Marth, and Samus and combines them into one. I've thought this for quite some time but watching Abadango play cemented it for me.
Of course, on the flipside, he also takes the worst qualities of Rosalina (tall, light, floaty, somewhat helpless at close range) and Luigi (traction problems, recovery can be exploited sometimes), but to what extent this matters remains to be seen.