It's hard to compare two countries that are so diverse. I'm pretty sure there are trans women in each country that are doing quite well and some in each that are going through hell.

First of all, as Greybeard points out, the USA is very diverse. Certain regions are generally considered more accepting: the Northeast, the Western parts of the West Coast states. But even in regions where bigots are in power on a state or even county level, you get individual communities or groups within a community that are tolerant and accepting. It all depends upon what mix of people you have and the history of the community or sub-community. There are good and bad people everywhere, and it's kind of the luck of the draw who prevails. "All politics is local," we say, and local can be very, very local. I hear of trans women -- and men and non-binaries -- who are managing okay in all kinds of places, including ones where you'd think they'd get burned at the stake on sight.

It also depends upon the trans woman. I think if you're able to make connections to people in your community, you do better because people have a harder time trashing someone they know as a person. And people tend to respond to you as you present yourself; it helps to go into encounters expecting the best of people. I've lived in my village (NYC suburb) for decades, and have always tried to be open and friendly and kind and assume the best of people, and so far, it has worked out well. The people who were aware of my existence in the first place have known me before, during, and after my transition, and they don't seem to have a problem with me.

It also depends upon what social group you are in. Black and hispanic trans women have more trouble, partly because their communities tend to be more socially conservative and are on the average less accepting of people being LGBT, and partly because Black and Hispanic people as a whole get treated pretty badly.

It's also hard to compare because we in the USA mostly know about conditions in the UK from news reports, whether in the mainstream media or in the various LGBT media, and the UK press doesn't seem to put much stock in being truthful (sort of like Fox News in the US.) It also appears to be pretty transphobic, and actually pretty bigoted and fond of bullying in general. We also hear rather nasty things about various politicians from all the major parties, but we don't hear much about how supportive or non-supportive each party is on the whole. (Well, I think I can guess how the UKIP is and maybe the Tories as well.) We hear about trans people who have suffered horrible mistreatment, but not those who are fully accepted and integrated into their communities. We can't really put it in perspective.