User experience is a funny thing. Some of the hugest hit sites are just plain ugly and even cumbersome: Craigslist, Hacker News, wimp.com, and many other very popular sites. I'm not just talking about aesthetics. Uploading photos on Craigslist is still like a flashback to the 90s. Yet millions of people practically live in Craigslist.
Also, good or poor UX is quite a soft notion mostly because different things are intuitive to different people. I hear people say they love to browse around Amazon, and I scratch my head. I think they must mean the AWS dashboard, which I love, but no, they mean that crappy bookstore.
There's a line of thinking that adoption can be be negatively correlated with easy UX. The idea is that you're less likely to quit something that you have struggled a little to learn. A think there's probably some data out there to support this phenomenon.
To answer your specific question, American Airlines is about the worst website experience I've had in a while. It just does not work. I had to phone someone to see if I booked the flight or not.
One very common UX problem I see on a lot of sites is lousy search. On most major content oriented websites the best way to find what you want it Google, not the sites built in search.