I've done courses with both. I'd say that for PPL level training there's little to choose between the professionalism and quality of the instructors in the two schools.
Bonus looks posher (uniforms, gold bars on instructors shoulders, nicer building), but I wouldn't read anything particualrly into that - good or bad.
Best thing is just make appointments to go and see both, and perhaps get a first flying lesson with both.
Enjoy Cranfield, it's a fantastic institution and the MSc programmes in particular are legendary. Take any subsidised flying opportunities that present from the university! As well as, not instead of, doing your PPL!
Incidentally - yes I agree that the PA38 is a nice training aeroplane, and Bonus have a number of them which are all perfectly adequate for PPL training.
Billins have a C150 and a couple of AA5s. Personally I much prefer the AA5 over the C150, even if it is a little more expensive. Roomier, better view, better handling, better instrument fit and better performance. On the other hand, if you are doing things as cheaply as possible, then there's nothing actually wrong with the C150 which is an excellent training aeroplane.
For basic PPL training, not much to choose between the AA5 and the PA38; the PA38 is lower performance with a more basic instrument fit, but I really wouldn't let that worry you either. Both are great for PPL training.
G