I can think of a few:
1. There will be a lot of geeks. I'm not being stereotypical, and I know a lot of non-geeks are clever too, but there'll be plenty of people who are anti-social, who would rather study than have fun, who were the teacher's pet at school and so on too.
2. I believe they're stricter about how well you achieve, and monitor you more closely. There's certainly more pressure.
3. People outside of there could very well think "well, they're a geek".
4. It's a pretty expensive place to be compared to some other Universities.
5. If wild parties are your thing, there'll probably be less than average (again, not everyone is boring, but there's a higher proportion of those types amongst straight A students than there is your average BBB student).
6. I think the holidays are shorter.
7. You'll come across more pompousity than elsewhere, especially if you're working class and from the inner city somewhere - There'll be more than the average level of private/boarding school types.
8. Location wise, there's better Universities than Cambridge and Oxford.
9. People may very well think you like boats.
10. Everyone I know who went on my college's Oxbridge visit was a geek, strictly religious, or the type who spent their dinnertimes sat next to the water cooler talking to the geeks and strictly religious discussing Maths. I wouldn't want to spend three years with them.
So basically, the weaknesses are mostly that you'll be around more anti-social, non-partying and middle-to-middle-upper-class types than at other Universities. Of course there'll be party types, but you'll have plenty of teacher's pets and wannabe MP's too.
That said, I'd go there if I had the GCSE grades and had been prepared for certain stages of my education better, but it doesn't bother me that I'm not.