Interesting choices. Boy, I'd hate to spend $1350 for one-way economy. I would most definitely choose EVA's $654 over UA's $1350. EVA's elite class from America to HKG is usually 2x economy fare, so that seems about right. Elite class on EVA is quite roomy actually, but personally I hesitate to pay several hundred $ more just cuz I'm cheap. Even then I would probably choose EVA's Elite via TPE over UA's nonstop esp if EVA still comes out cheaper as in this case.
Contrary to what jib says, I love the timing of EVA's Asia-bound flights. You put in a full day of work, go home and pack, and then you get to Asia early by sleeping on the plane instead of sleeping at home and then wasting a day on the plane. I usually fly cramped in the back of the plane on EVA or Cathay going to HKG, but I almost always arrive in TPE/HKG feeling fairly well-rested cuz of the timing of the flights being conducive to sleep. But again, this is all matter of personal preference. What works for me may not work for you.
UA is not too bad. Rather, I'd say Asian carriers (esp NH, OZ and probably BR soon as they go to 10-abreast on 777's) are sinking down to UA/AC's standard, at least in terms of food and hard product.