Statistically the Chinese national airlines are more dangerous that most other alternatives, however the numbers are still grossly in your favor. It may sound bad to say that, for example, China Airlines has 6 times the accident rate or fatality rate of Cathay or whomever, but it's still plenty safe.
Still, I only fly them when I have to, and would readily pay $300 extra to fly something else. Services are sub-par, but we're all used to that on long flights. Pilots execute some of the roughest landings I've been in, but if it's the only schedule that works (or if it's grossly cheaper, like half price maybe) go ahead a fly it, just realize you're in for a grind.
I concur with the other posters that one should avoid U.S. customs and immigration whenever possible. They're not bad folks but it's one of the most tedious places in world to try and clear, and if you're just having to do that for a connecting flight? Yech!