Birmingham is far stronger for engineering. Exeter is pretty mediocre for it (for the main campus) and is not especially well known for engineering (outside of the Cornwall campus and mining engineering and related areas). The level of incoming knowledge among students is pretty low according to one of my lecturers there and so they don't end up teaching some content that would normally be taught in first year until third year...
Also Exeter is still miles away from any beach where people surf at, so it's not like you can just finish up your lectures and then go surfing. The surf society just organised trips on weekends now and then (mostly at the end of term/reading week as I recall - you always saw them gathered at the bottom of the hill with the surf gear getting it into/onto the minivan they were using) that I noticed when I was there, because there was no practical way to get to any kind of beach except renting a minivan and taking a bunch of the students there as a weekend outing. You would likely have pretty similar experiences in this regard at Birmingham.
The Cornwall campus might be more favourable for that though as I believe it is a lot closer to accessibly coastline, and is stronger for certain kinds of engineering to boot. But if you've applied for the main (Streatham) campus, I can't see much in justifying it over Birmingham even if you are into surfing a lot.