Hi Trainee pilot
I finished my training at Oxford about 6 months ago, and i would have to say that the quality of flying instruction was of a high standard. I feel the most critical part of the training is most probably the conversion onto the twin and the IRT. Oxford have this pool of twin instructors with great experience and knowledge, which perhaps smaller flying schools do not.
The advantage of doing your flying training at a place like Oxford is that as you mentioned, it is used by airlines and they are happy with the quality of student they are getting out.