I think it does make a difference which one you select. If Oxford had 33% more candidates then your chances go down by 33%.
No, not really. 5000 people apply. 50 are selected. Doesn't matter which FTO each candidate goes to. Admittedly you might stand a slightly better chance of going further in the competition (correct name for it?
), but in terms of actual overall success, there is very little statistical difference. In other words, the candidates who were chosen last time around probably still would have been had they all attended different schools from the ones they did. Quality to that extent shines through.