I'm laughing cos mad_jock and Cows Getting Bigger said pretty much what I had originally written and then deleted.
Oxford might give you a slight advantage if you want an airline job. In my experience it will look poor on your CV if you're looking for an FI job compared to an FI from the other places mentioned.
The two Oxford graduates I have flown with had very little situational awareness in the VFR environment. They may have been fine heading for Ryanair but their ability to fly a visual circuit and plan for separation in non-controlled airspace was not good. Even if your previous training was elsewhere, to choose OAA as a training provider shows no understanding or knowledge of the real world.