Honestly, they're both not very good moves. Psychic and Psyshock outperform either imo. However, Zen Headbutt is more popular for a few reasons:
- a slight increase in power at the cost of accuracy, and
- a lot more Pokemon have access to ZH as compared to Psycho Cut
- a chance to flinch
For what it's worth, personally I feel Psycho Cut > Zen Headbutt. The crit hit ratio can be pretty useful, and good accuracy means that more hits are guaranteed more often. Which, if they turn critical, will definitely increase damage output as the turns accumulate. Given how few Pokemon actually have access to it, however, means that Zen Headbutt will remain popular for the time being.
