I would guess the popularity of the red bow tie version may be because the 11th Doctor tends to be seen wearing a red bow tie [occasionally other colours but mostly red]. However, in FiM the only time Time Turner has a colour and tie on the tie is green but its a tie and not a bow tie. I know a lot of people seem to compare Dr Whooves to the 10th Doctor but as he is not a bow tie kind of guy...I am just making the assumption that a comparison with #11 may be the reason all the red tie versions are purchased a head of the green tie versions.
But outside that as others have said the cases are 12 green and 12 red [with 11 red regular and 1 red translucent] - so it should be a 50/50 shot.