I think UA will be your better bet. More flights to Europe and Asia will give you more flexibility. From your note it seems that miles are important. (Least hassle is another issue.) If you are able to spare a few hours in the quest for miles on the European flights fly SEA to LAX then to LHR, etc.. This amounts to almost 2000 miles more/RT. You can also fly to SFO, but it's fewer miles and you need to deal with the shuttle and its poor on time performance.

I try to do this on all my European flights. The only time I question my sanity is when I'm returning in coach and we fly South, past Seattle and I realize I'm 4+ hours from getting home.