Congratulations on your engagement!
The immigration processes for both countries have pros and cons.
For the US, it's easier to qualify (if you do not meet the financial requirements - which are low, you are allowed a third party sponsor). However, it takes 8 to 10 months to go through the process. I believe the fees are also a decent amount less than the UK fees. I'm not sure on the time frame, but I believe it's somewhere between three to five years until your fiance will qualify for US citizenship.
For the UK, there are very strict financial requirements that only your fiance can sponsor (no 3rd party sponsor). This is especially hard to meet if your fiance lives in the US and moves back to the UK. Your fiance will need to have made £18,600 in the previous 12 months in the US
AND have a UK job offer starting within 3 months making at least £18,600. The problem we see here often is the UK sponsor struggles to obtain a job offer without being physically present in the UK. Unfortunately what happens is the UK citizen has to return to the UK, obtain employment, and work in that job for six months before your visa can be applied for. However, if you meet the requirement, the visa is usually issued within a month. The visa's for the UK (you'll need several before qualifying for citizenship) are very expensive. It takes five years to qualify for ILR (free from immigration rules) before you can apply for UK citizenship. I would plan on living in the UK for 6 years by the time you have it (as application processing will slow things down and not make it 5 years exactly).
You don't really need dual citizenship. Just so long as one of you has permission to live and work in the other's country, you're good to go.
LA to Milton Keynes will be quite the culture shock!
