I may be wrong, but I have a feeling it can be harder to get a visa to move to the US than to move to the UK.
If you will be moving to the UK, you can either apply for the fiance visa, move to the UK, get married within 6 months and then apply for the marriage/spousal visa, or your fiancee can fly to the US as a visitor, you can get married in the US, apply for the spousal visa and then you can move to the UK.
However, if you wish to marry in the US and then continue to live in the US, your fiancee will need to get a fiance visa and then you will only have 90 days in which to get married and then apply for the spousal visa.
A comparison of visa processing time: I believe that many people on this board have had their fiance/spousal visas issued within a few days to a couple of weeks or so. The US Embassy website says you should allow 3-6 months after the petition (that the US citizen fills out within the US) has been processed for the visa to be issued!