Is it better to work out one muscle group a day once a week or two a day twice a week?

For the second program you would be resting your muscle for too long which will ruin the point of working out very hard.

For the first program is it...

Mon - back/biceps

Tue - legs/shoulders

Wed - chest/triceps

Thursday - back/biceps

Fri - legs/shoulders

Sat - chest/triceps

Sun - rest

If it is then the first option will benefit you more than the second option. 2 days is enough rest to give to your muscles. To be honest though, if one way works for you then it doesn't matter which one to go with. There are thousands of ways you could plan your workout and they can all work in there ways. So for example you could try something like upper body, lower body, rest, which is a three days routine giving 2 days of rest before working on the muscles again.

your best to train each muscle 1-2 a week

1-2 muscles a workout

something like this

mon chest

tue biceps triceps

wed back

thur shoulders

fri legs

First is better since you get rest days in between