The choice isn't just between Bristol and Oxford of course. There are other upcoming schools which offer a radically different approach to ATPL theory.
However, to answer your question the key difference between the Bristol and Oxford approach is in the depth of coverage of the material.
Oxford's notes are very comprehensive - rather too much so for some people's liking. But the advantage is that you get a very thorough grounding in the subjects.
Bristol's notes are significantly less deep. The advantage is a more focussed approach to exam passing. The disadvantage is that they don't necessarily promote the most thorough professional grounding.
Don't fall into the trap of thinking that ATPL theory is just a hurde to be jumped. A lot of this knowledge underpins everything that you subsequently do. It's important not to just 'learn and dump'.