Debate Confusion vs Psyco Cut on Mewtwo

If you're using it as a fighting (or poison) type counter use C/SB, as a gym attacker either C/FB or PS/FB is fine, and anything else should be PC/SB.

I prefer faster moves for the sole reason of it being easier to dodge with them

If you have too much TMs, change your Mewtwo's moves with the current Raid Bosses.
My Mewtwo used to have Confusion/Shadowball and he served me well vs Raikou/Kyogre/Groudon (+ a few 3* Raids), but I've changed him to Psycho Cut when Lugia arrived because his time to win rises enough to make it worth it for me.

In general I'd say:

Psycho Cut: Makes him a good ghost/fighting specialist.
If psychic is resisted and/or the charge attack (focusblast/shadowball) hits super effective (or is weather boosted)

Confusion: Makes him a great generalist and part time ghost/fighting specialist.

Doesn't matter: If the charge move is super effective while the fast attack hits neutral they will perform pretty much the same (no weather bonus)

Once the dodge glitch is fixed I'll be moving my C to PC for Mewtwo. But for now Confusion to get as much DPS out as possible.

Since you have two and are indecisive, one could have Psycho Cut, the other Confusion

Alakazam

Using Confusion in gyms bores me to tears because I'm a dodger. It's Psycho Cut for me, even though it does less DPS in most situations.

There should be no debate - despite confusion having a slightly higher dps than PC , it gives much less energy per second and doesn't allow for dodging. Psycho cut is by far mewtwos fast move of choice
I prefer it paired with focus blast for gym attacking use