What are the differences between getting married in the US as opposed to the UK?
Getting married in the US is usually the easiest and cheapest, immigration-wise. Your fiance can come to the US to get married without a visa (he can just travel on the visa waiver problem) as long as he's not planning to live in the US after the wedding. Then, once you are married, you can apply for a spousal visa for the UK (costs about $1,000), which is valid for 27 months and allows you to work immediately in the UK.
If you want to marry in the UK, then you'll need a visa to do so... you'll need a fiance visa, which costs about $1,000, is valid for 6 months and does not allow you to work in the UK. Then, once you are married, you will then need to apply for a 2-year spousal visa in the UK which does allow you to work (currently costs £475 by post, but takes about 4 months to be processed and you cannot work during that time, or £730 in person for a same-day decision and you can work as soon as you have your visa and ID card).
So, in terms of visa costs:
Marry in the US: about $1,000 for a spousal visa (but there's also the cost of his flight to the US for the wedding)
Marry in the UK: about $1,000 for a fiance visa, then another £475 or £730 for a spousal visa after the wedding.
Do you think one would be favorable over the other when it comes to the visa application?
My friend thinks that it may make for an easier transaction if we get married in the UK or a UK territory. Will it make a difference?
It won't matter either way in terms of how immigration views it, but getting married in the UK involves getting 2 UK visas and getting married in the US only involves getting 1 UK visa.
The main factors for your decision will probably be based on your personal circumstances: is it cheaper for him to fly to the US for the wedding than for you to pay out for 2 visas if you marry in the UK? Are there specific people you want to be present at the wedding which will determine which country you marry in? Do you want to be able to work in the UK immediately, or are you happy to wait a few months (after you have arrived in the UK) until you are married and have the right visa?