ak224. If you detect a small degree of cynicism in some of the responses, it's because your line of questioning is very similar to another member, Afraz, who pops up every now and then and repeatedly asks the same question.
To answer your question, the 'prestigious' schools as you call them would obviously love you to think that training with them gives you a better chance of an airline job. I'm sure you can work out why they do this, but for anyone who can't, Oxford's course (currently £66,000) or FTE's (£81,000) will give you essentially the same qualification as modular training with a number of smaller schools, which can be done for more like £45,000. They need to justify the extra cost somehow, and dangling the prospect of a shiny jet job in front of you is part of the act. Ask them if they can guarantee you an airline job, and they wont - because they can't - but there will be plenty of subtle nods and winks. In case the message isn't obvious enough, Oxfords's homepage has a nice big picture of a 767, and FTE show you what an Airbus looks like. Be in no doubt, it's slick marketing - nothing more.
When airlines are recruiting, candidates from 'lesser' schools are just as likely to get jobs as those with Oxford or FTE on their CV. The (very small) school I trained at does not have any pictures of jets on its website - but it does have a photo of their dog, which I rather liked. Despite this handicap, they managed to get five ex-students interviewed with a fairly large UK airline - and four of us got jobs as a result - within a single month last year. The key phrase is 'when airlines are recruiting.' Right now they are not, and it doesn't matter whether you trained at Oxford, NASA or Much Piddling In The Marsh Flying Club, there are no jobs out there. Nor will there be many for low-hours pilots for at least the next 2-3 years.
Timing, contacts and determination are all far more important keys to success in this game than where or how you trained.