Well, Exeter is 30.6% privately educated. Bristol is 35.5%. That's just the raw stats; if you've visited either place, you'd have a pretty strong sense of the difference. Exeter also has more international students, at 25% to Bristol's 23%.
Even still, I don't think you should decline to attend a uni based on its having lots of a certain type of people. An "us vs them" mentality is unhealthy, although ripe in some comp-educated students. I was never personally bothered by it in the slightest.