Hi Ben! Thanks for starting the blog. I'm excited to hear more about your Asia trips, I've been waiting for a blog that focused more on US-Asia travel!
depending on which Asia country you are going and from where here in US.my experience overall UA and AA miles are very useful as I am here in Seattle. if you live in East/Middle side, AA is more flex due to the partner like Cathy Pacific which is much more superior Business/First Class than america airlines.for example, there is a direct flight from Seattle to Tokyo(NRT) and I like UA miles better than AA, even though AA charges less miles, the connection to Dallas doesn't work out for me.so, it varies from where are you and where are you going? :-) but overall, UA/AA are your best friends in terms of Asia trips.
Ben,I am in Houston and would like to fly to Singapore, Shanghai or Hongkong
I don't think IAH has AA rewards to HKG/SIN, you may call them to confirm. however, IAH(houston) has 70k reward coach to Shanghai and United will cost you 65k. if you fly to Japan, AA always has space and as low as 65k. in your case, i'd say stick to UA for those destinations.