BA definetly
I did Taipei-> SFO -> IAD and back last year with United, it was one of the most horrible experiences I have ever had.
Check in a TPE I was told I might not get a seat (been booked for 6 weeks).
SFO transfer was okay
Waited at the 'right' carosel for the flight in IAD for 30 mins and didn't see my bag, after everyone else from the flight had left I used the machines to discover my bag had been sent to a different carosel to everyone else.
Coming back the auto check in machines took my wifes details and checked in two light bags for her but barfed at mine. After waiting in 3 different queues for 30+ mins I finally found someone who would check me in but now I had both 'heavy' bags and so even thou our total was 20kg less than the limit we got hit with excess baggage fees. After getting to the terminal 2hrs before the flight I still only made it to the plane after everyone else had boarded. On top of that I got flagged for the 'extra security' checks and was separated from the missus who got quite upset.
Transfer at SFO was stressful, only a mini bus to move people from terminal to terminal and if you walked you had to leave air side and then be checked back via security.
I will never travel United again unless there are no other options. Never had any trouble with BA, may not be the nicest but their people seem much more helpful.