Everyone says that the school makes no difference, but ultimately of course it does.
For integrated I acquiesce. Some people may perceive the quality of schooling as being better at Oxford. I wager that any perceptions regarding a schools superiority are held primarily by its students (past and present) and management rather than potential employers; which would parallel opinions regarding Oxbridge and the real world (except the Civil Service) but that is another argument.
For modular, surely the discussion is nearly irrelevant as you already need a PPL and 150 hours before starting the CPL as structured hour building is considered a crucial part of a low-houred ATPL(F)ers CV (so I am told). For the theory stuff: well you are at home for the vast majority of the time and you either know the stuff or you don't (I imagine). It would hard to argue that a first time passer has had a lower quality of training than an Oxford somebody who needed to retake two subjects.