In regards to Mewtwo, it's definitely one of the most versatile mons in the game. But to be honest, I've never been a fan of 4 attack LO Mewtwo. I actually generally run the Standard CM set with Leftovers > Life Orb. Mewtwo is surprisingly bulky and I like being able to recover HP.
Taunt + CM Mewtwo is great against stall and the like, but the fact that it forces you to choose between 2 coverage moves out of what feels like an endless array of attacks is it's biggest problem. StallTwo can also be very troublesome if you're not expecting it. I ran it a lot back in D/P when Jibaku first introduced it to me and it was a lot of fun.
But yeah there's a lot to be said about Mewtwo. It just does it's job so well.
I might be using it wrong, but whenever I use Mewtwo I'm generally underwhelmed at its performance X_X. I mean I guess its strong but its so difficult to get in, and with Genesect spamming U-turns everywhere getting a Calm Mind is so hard without having 70%+ of your HP chipped off in the process. I know Taunt + CM was effective last gen, but this gen introducing Dragon Tail made it a lot less effective for me when I used it (I did use Lefties > Life Orb in this scenario though). Since CM is so hard to pull off, I like the Life Orb + 4 attacks or Life Orb + 3 Attacks and Recover more. Stall Two is a cool stall breaker too, that is if you can avoid getting Dragon Tailed out into Toxic Spikes. Don't get me wrong though, with Tentacruel or Poison Arceus or reliable spin support (ironically this is the least reliable option) Stall Two a fine mon, capable of stomaching even Soul Dew Draco Meteors from Latios at full HP when Light Screen's not up!
Ironically I'm more terrified when I play against Mewtwo then when I use Mewtwo (which is why I've been saying I might be using it wrong throughout this post X_X). Mewtwo after a Calm Mind has very little to check it. The closest things that can come to countering it are Psychic Arceus, Dark Arceus (who btw completely outclasses Psychic Arceus IMO), and Specially Defensive Giratina-a. The first two get 2HKOed by Mewtwo's moves but they can KO Mewtwo before getting KOed. Specially Defensive Giratina-a doesn't care about +1 Ice Beam (well it'll do a good chunk) but it can phaze Mewtwo out and rest later. In theory this DOES mean it did its job as a wall breaker, but still... Checking Mewtwo is a lot easier though. Even though Mewtwo has that elitist base 130 Speed tier, its prey to Choice Scarf mons. While it gets a lot harder after Mewtwo uses Calm Mind, its still possible. Physical Choice Scarf users (Genesect, Garchomp, Zekrom, etc.) can OHKO Mewtwo before it OHKOes them. Switching them in is something else though, which is why they are "checks" and not "counters".
What sucks about Mewtwo the most though, in my opinion is, his Psychic typing. One of the most reliable ways to set something up in Ubers or get them a free switch is with Wobbufett. Wobbufett and Mewtwo share the same typing, meaning its a little harder to lure a move that Wobba can setup on then Mewtwo (this completely changes when Encoring setup moves though), the type-stacking isn't fun either, not to mention Psychic is a terrible defensive typing, scoring resistances to Fighting and Psychic type attacks! The most uncommon thing in Ubers (I dare you to look up Psychic Arceus's statistics)! It does give STAB to Mewtwo's Psystrike though, which I guess is cool considering it lets you 2HKO Chansey. Its coverage outside that is "ok" I guess, since it hits defense Mewtwo can now also defeat Fighting Arceus, Palkia, Reshiram, Ho-oh and Kyogre. Psychic STAB is something no one would dream of using if Mewtwo didn't get Psystrike though.
But Faint, since you have stated you can use Mewtwo successfully, I ask you how? Whenever I use it I end up being unimpressed. How did you support it to get such successful results :P?