I spent the first 9 or so years of my life in N America and the rest, mostly, in the UK.
With respect, from my observations, the most notable difference is that British people are very reserved and along with that, very conservative. I don't believe British people are intolerant, especially of race. But they are cautious of any innovations that might impinge upon their own lives. Clearly, there will be many individual exceptions. I'm obviously referring to the general attitudes. But generally, if it doesn't directly affect them, most British people, especially English people, are often quite interested in other ideas and ideals. Though in the case of race or sexuality, this curiosity can sometimes be misinterpreted as intrusive interference.
Americans especially, are obsessed with the past and controlling the future. They seem to be continually prepared to abandon the present, even the values of the past, in the present, so they can restore what they see as some sort of traditional ideal in the future. Form a people who have so much to enjoy from the present, an astonishing environment, wealth beyond dreams, opportunities and mostly wonderful people, their readiness to send their sons to fight and die in wars that are of no concern to them at all, even to attack each other at times, is sad and surprising.
I don't accept the arguments of gay marriage. I have personally, I'm sure like many, avoided the gay marriage debate quite deliberately and will try to continue to do so. But the current and I suggest, infinitely more sensible focus, in the UK, is currently upon extending civil partnerships to mixed sex marriages here in the UK.
This is a long over due measure. A large part currently holding it up, is the section of the gay lobby who want gay marriage. But the biggest obstacle to marriage equality is the CofE. This is still the established church in England and hold enormous power, especially in marriage law. The long term solution is to disestablish the church of course, but that can never happen in the lifetime of the Queen since she made it part of her coronation vows to uphold the position of the CofE.