I would say in terms of usefulness, Focus Blast or Psychic is the way to go. Although Machamp is the better option for clearing gyms, PC/FB Mewtwo does a lot of damage and is fun to use as a gym clearer. I have a maxed out 98iv FB Mewtwo and I use him all the time. As you mentioned, Psychic is still a great option for Machamp solos. In fact, I used a couple of them today. TB Mewtwo is actually a nice option for those who do not have any powered up Raikou or Zapdos. It really depends on what you are using him for and/or what you may be lacking in each of those types.
Mewtwo Conundrum
I've been looking at my 96% raid catch last month and have been wondering that to do with it. After looking at all the moves and how they compare with other pokemon, I felt I should share my results and conclusions as I dont think im alone in not knowing what to do with these mewtwo.
With gen 4's new pokemon, in particular the nonlegendaries, it kinda looks like mewtwo's psychic and legacy shadow ball sets will be the only worth while sets for mewtwo, given how massively outclassed mewtwo is by even nonlegendaries. (We dont have the gen 4 evolutions yet, but these possibilities still exist and do seem likely to happen given the shear number of them)
With focus blast, a double fighting machamp already beats it DPS wise and on the potion efficient gym clearing side, MM metagross does that a lot better, with both having much more over all use in the meta
For ice, mamoswine, weavile and glaceon are all easy to get a cheap options of options that significantly out DPS to mewtwo with ice beam.
Thunderbolt, while not bad, electric is a very niche type to begin with, as well as much like ice, its outclassed by 3 nonlegendaries in gen 4, luxray, magnazone and Electavire, as well as legendaries like legacy TS and nonlegacy zapdos, and Raikou which we have had for longer.
Flamethrower mewtwo...theres too many things to list that outclassed this even prior to gen 4
Hyperbeam....Why havent you gotten rid of this move yet from your previous EX mewtwo?
Psychic, despite its limited effectiveness and usage, it still the best coutner for machamp (though there are other legendaries that can deal with it that also have wider use, as well as there are viable psychic nonlegendaries that are less expensive, mewtwo is still the best) which on its own might more than justifies powering up for solos, as well as is sufficient for gengar raids if lacking shadow ball mewtwo. Its only threat is mewtwo itself with psystrike (which currently isnt that good, bearly edging out psychic presently) or some other limited time psychic move, likely its use will hinge on your psychic/machamp situation
Without shadow ball and with the fantastic gen 4 pokemon, mewtwo's use beyond machamp took a big hit before it could be useful, it might have been a serviceable protean if you didnt mind the TM intensive cost, or Ice beam could have had it chance to shine had we gotten rayquaza now, and while ice beam isnt a terrible move against giratina, we're all loaded up on lick gengar and likely the stardust and candy to power them up.
Answers
I think the most consistent answer you'll get will be Psychic for sure. Niche use aside, it's currently the best of the best for psychic types and likely will be throughout each generation. While Alakazam and Espeon are cheaper options that will get the job done, they're not known for taking hits. I wouldn't even worry about Psystrike right now as there's no telling when they plan to release it, if they ever do.
We still don't know how cheap or easy the Gen 4 ice types will be. Favoring Ice Beam will depend entirely on their availability when the next doubly weak to ice target presents itself.
Thunderbolt Mewtwo is about the 4th best overall counter to Blizzard Kyogre for what that's worth.
lol Flamethrower.
People like Focus Blast. My gym area isn't crazy enough for me to mandate needing one so take their word for it.
Another point that's a long, long way off to consider are megas. Mewtwo gets two of them that are pants-shittingly busted. All of these moves will need evaluation again once we see how Megas are handled, but they could stack up to be absolute units.
I dont think we realy should take megas into consideration, namely because their stats are so absurd, Niantic would must have some idea that if they made mega's thing, their stats would need to be nerfed. Even with something like super effective damage, given how absolutely rediculous m mewtwo y, M quaza and the like are, few to nothing could compete with them, and as such there'd be no money to make from adding pokemon because nothing could possibly come close to them. look how great the neutral DPS of those two pokemon non-mega already are, viable in situations even without weather boost. There would need to be some sort of nerf in place on them of the entire game would literally devolve to how many mega rayquaza/mewtwo/salamence/tyrantiar/metagross or primal groudon and kyogre you have, they would completely outstat almost anything else, look at the nearly 7k mega mewtwo y's CP would be un nerfed, theres no way something like that would be allowed to stay, get a team of them and never need to raid almost anything else again.
"absolute units?"
I remember you at one point basing a lot of your future-proofing on megas becoming a thing. Why the change in tone?
At any rate, if megas would work anything like they do in the main series there's not a chance in hell we could assemble teams of them. I realize Niantic has made a questionable amount of goof-ups with regard to base Pokemon info lately but even they'd have to see the absurdity of that. One mega per trainer per fight. I wouldn't be surprised if past a higher CP window (say > 6k) they drop an 18% nerf to attack and defense (stamina stays the same since potentially nerfing that mid-fight would be bullshit, which in Mewtwo's case would be a standard 9% nerf. It's also the only stat unchanged when a Pokemon undergoes mega evolution).
Because I realized absolutely busted they'd be, and how much they'd completely outpace anything else. It wouldn't make any sense for niantic to keep megas as they're projected to be without nerfing them.
one meg per battle seems like what they'd do, but knowing niantic, they'd probably goof up and make it so you can use one mega per team. 18% nerf would make sense, possibly keep their stat are are but can only use them for a few seconds, or something else entirely for a nerf, like requiring some massive amount of candy to use (like 400 candy to get a mega), but it doesnt seem like it'd be a separate entity all together.
As others have pointed out, Psychic is likely the best choice in Mewtwo's current movepool, as it's likely never getting outclassed as the top Psychic-type attacker.
Aside from that, the only other use Mewtwo has comes from that fact that it can be TM'd, if you have a surplus of them, to a variety of different charge moves. This can allow a high level Mewtwo to slot-in to teams for a number of different encounters and perform decently well. It will never be the best option in these roles, but some players may find it useful to throw some TMs at Mewtwo to give it Ice Beam or Thunderbolt, as opposed to sinking dust/candy leveling up another Ice/Electric-type attacker. So if we get Rayquaza back as a raid boss, for example, some players might TM their high level non-legacy Mewtwo to Ice Beam to round out their team, rather than sink resources into another Ice-type.
Unless it changes, GP has Psystrike listed as a 2-bar 100dmg move with a 4.4s cool down and the damage window at the 3s mark. So while it will outperform Psychic in terms of pure DPS output and by virtue of being a 2-bar move, there's a fair chance that it could underperform in PvP, as it will be significantly easier to dodge than Psychic. In addition, since we just had an entire month of Mewtwo raids, my guess is that Psystrike Mewtwo (if introduced via a raid day) won't be available in the very near future.
Also, Gen 7 is a long ways away, so I don't think it's reasonable to discount Mewtwo because of a potential threat that won't be available in Go for years.
That said, Psychic Mewtwo currently has very limited uses, so it's understandable not investing heavily in one due to that.
didnt know the exact specifications on Psystrike, all I heard was it was a slightly improved psychic DPS wise, and thats what matters most in raids. PVP wasnt something I overly thought about given its not currently in the game and psychic wont have much use in there as well, machamp and fighting in general doesnt have the bulk and DPS to deal with many of the projected heavy hitters as well as most legendaries people will be using, like mewtwo itself, its other movesets likely will be better than psychic
Gen 7 I agree is a long way away, but thats why I put in parentheses, its distant but is there, its more immediate threat is itself if psystrike even if it doesnt receives some kind of buff, most will prefer the 2 bar nature most likely, the relationship between the two moves seems not that dissimilar to outrage v draco meteor. The limited match ups is another thing to consider, given the good legendaries we'll be getting in gen 4, dialga, palkia, darkrai specifically.
Good points, close to how I will play the game forward. I think it is quite safe to power up several high IV Mewtwos with the most useful moves to say level 30, as they can always be TM'ed at a later stage. Ice beam M2 is already useful in Giratina raids, to slot in with dragons, Gengars, Tyranitars and M2 SB. I trio Giratina most of the time, and then there is a need for 9-10 good mons for each user.