This is a really tough call. I've been there.
Eight or nine years ago now we were at a point where one of us had to move to the other's country. We both assumed, at the time, that I would go to his (Sweden) because they let in practically everyone with any sort of tie to the country and cmon, Sweden, right!? On a whim I had him apply for the US Diversity Visa Lottery, not expecting anything out of that. Oh but fate had a different plan and his name was pulled and he had the chance to jump to the head of the green card line.
I didn't really want to continue living in the US, and had always wanted to move back to Europe/UK but the rational part of me said this was something that he needed to do for a variety of reasons - better employment market, housing, chance for him to finish university, etc. I reasoned that we would do the time in the US for him to get citizenship, that Europe would always be there, etc. At the time I was also in the midst of moving back to my home state, and was unemployed.
So we agreed for him to accept the GC and move to the US - my parents served as sponsors. And for the next SIX YEARS (we aren't married so he had a 5 year period) I felt uneasy - always waiting for my career to start, always wishing I was somewhere else, trying to make the best of places that are lovely places to live but just didn't feel like home. The economic crash happened, setting us back another year. But we made it in the end and he is now a US citizen too and looking back we achieved a lot of what we set out to do during that time, but sometimes I also feel like I wasted a lot of my 30s waiting for my life to begin.
We finally moved to the UK and its been rough, and we've considered moving to Sweden for me to do time there (3 years to citizenship) but we decided not to because we didn't want to put off our dream of living in London any more (amongst plenty of other reasons from poor job market/xenophobia/weather). And as hard as its been, it is still comforting to know that we can pick up and move at any time back to the US. You would get both sides of your immigration situation solved in the amount of time it took us to do one.
I think what I am saying is: its an awful dilemma, but if you recognize it for being part of your long term plan, and work to make the most of that time, once you are through the other side there is a security that can be worth it. I'm not saying it was easy to squish down those dreams, but I also spent the time with aging relatives I hadn't seen in many years (one of whom we almost lost this week), spent time with my parents, tried new sports, did some road trips. I took jobs that prepared me to get decent jobs here, he finished school and did work that got him a job here, etc. We made the best of it. Who knows what the future holds? Having the immigration flexibility though... that is almost priceless.
What I would suggest is maybe mapping out what you would want to achieve in the next three years (short term) and the long term view. If you went to the US, what would you want to accomplish that would set you up well for the future, either there or in your travels? What or who would be important to you in that time? What about work, part time or full time, that would cover your medical costs? What about financials and retirement planning?
I would also suggest that now is probably as good as its going to get in the new economic world order to make something happen in the US. The last three years in the UK were an economic pit - this time around you would be entering the US on an upswing - fuel prices low, unemployment coming down, base wages going up (for some) etc etc. I'm guessing you could find something to supplement the cost of getting further education for your field or to help cover medical costs or put something away.
Only you can make the final decision, but if it were me I would head to the US and get it over and done with. Three years is almost nothing in the grand scheme of things, but use the time wisely and you could have yourself set up well for the long term.