Well, there's a couple of things on both sides.
Freedom of speech (albiet socially negotiated)
multicultural sociey (although not really very diverse in Cornwall)
We have interesting weather (you never know what it'd do from one minute to the next - stereotypical small talk for us Brits)
British films - Like American films, only a slightly different sense of humour and greater emphasis on irony.
NHS - If we get hurt, we get help no matter how poor you are (although you may have to wait 2 years)...
Government - incompetent and decietful
Cost of living - Whilst not being unbearable like some other countries, it's can still get quite unfair, especially when you live in a part of the country with the highest house prices and the lowest wages - you don't leave home until you're 33! (If you're lucky!)
Geo political forces - We're constantly torn between US and Europe, both looking like giants that don't really care about what the British want or need.
CHAV's and racism - Whilst not exclusively British, we do have plenty of racism here, and the CHAV's make a mockery of the Justice system.
Nationalism - A whole heap of problems there.
Overall, if there was actually a place on Earth whereby the politicians were out for the people rather than profits, where pride is secondary to logic and where the state is run as a social backbone and not as a buisness, I would prefer to move there. But since it's not going to happen any time soon, I think I'll just grin and bear it here.