Exeter is in the Top 5 for it's business school now I believe, so it has a reputation to rival Bristol's.
I live in Bristol now, and attended Exeter Uni. Bristol is a bigger city, more shops, more nightlife etc, however Exeter is also good for shopping and there's enough variety for going out. Also the SU at Exeter is brilliant, and the new forum at Exeter is simply fantastic.
Bristol and Exeter are very different in that Exeter is a campus University and Bristol is not. Exeter is near the coast so you can go to the beach in the summer, however in Bristol there's not many beaches/attractions to choose from. It comes down to personal preference really, both are great uni's. Personally I wanted a campus university with a great community feel and to be near the sea, so Exeter swung it for me.