Which is better for gym attacking, Mewtwo or Machamp?

Whichever.

I have a preference for Machamp, because:

1) Machamp has a fighting quick attack, which is more efficient than a psychic QA and a fighting CA.

2) Machamp can be powered up with Machamp candy and doesn't need rare candy.

They are both really good, but those two points give Machamp the edge IMHO.

Machamp, provided you dodge DG from Blissey.

Machamp will get the job done faster (and with much smaller candy/dust investment) at the cost of being less tanky against all the psychic/fairy moves commonly carried by the normal-type tanks in gyms. So my vote goes to Machamp.

For gym attacking I always prefer mons with multi-bar charged moves (so in this case, Machamp), since it leads to a lot less wasted energy, especially when fighting demotivated defenders.

Overall, Machamp.
You can still use a personal strategy. For example, when the Blissey has full motivation, I start with my Mewtwo. After that first fight, Machamp does much better because of the double charge move, and the Confusions don't hit as hard. This is particularly useful when I'm low on potions.

I'm using Karate chop Machamp. Dodge friendly and fast

Note that if you are not trying to dodge, Confusion/Focus Blast is better than Psycho Cut/Focus Blast. Psycho Cut charges energy faster, but makes you more reliant on using the charge move for damage. If there are any low motivated defenders or anything resistant to fighting mixed in then you will waste time/energy. The main advantage for Psycho Cut is dodging or if you are attacking something that resists psychic.

I use both, but prefer my maxed PC/FB Mewtwo(s). I use the Machamps for cleanup, and when a Blissey is being berried.

What is a Mewtwo?

Neither one is strictly better than the other so it comes down to what you personally value.
Machamp is faster, uses more potions, has less dodge friendly fast moves and more dodge friendly charge moves (C is slowish, DP is fast).
Mewtwo is slower, uses less potions, has more dodge friendly fast moves and less dodge friendly charge moves (PC is super fast, FB is glacial, you often can't fire it completely safe from getting hit with DG before recovery).

I prefer Machamp for fighting normals, my powered Mewtwo is currently a PC/SB swiss army knife that can defeat anything Machamp struggles with.