A bright spark actually wrote to a large number of airlines and asked them that very question - from the responses it was clear that in general there is no preference. The only preference towards integrated expressed was on boundary conditions of
- low hours AND
- company who already have a training 'agreement' with a school - e.g. CTC for example easyJet
So, that applies only to those on the specific scheme.
I can't find the link now but it was posted on here some time ago. Ask yourself what you are most comfortable doing, and remember that binary thinking (e.g. If I go with Oxford I will get a job, if I don't I won't) is a bad thing!
Andy