In my opinion, they're both not very good indicators of an institution's quality.
League tables are compiled from out-dated and irrelevant statistics, sometimes with arbitrary scores thrown into the equation.
Prestige mostly comes from history and isn't necessarily representative of the institution as it now stands.
Both are measures which a small number of employers naively use to distinguish between candidates, but with the exception of a few select fields/employers, the difference between going to Nottingham and Warwick is nil.
From league tables, pick the factors that are actually important to you - employability prospects, teaching quality, research rating, etc. I personally don't feel like average UCAS points on entry is useful for example as it doesn't recognise academic ability as it is often portrayed.
Other than that, choose somewhere with a course structure and content you'll like, and where you think you'll enjoy studying the most - you're going to spend 3+ years there after all.
On the campus note, I think Nottingham's are some of the most impressive by far, and they win enough awards each year to prove it. A couple of others may compete, but they really are stunning tbf.