I'm based in Europe and have both an AA , a BA and an IB Avios account.
I credited everything to AA until last year because AA was a better program for both redemptions as well as status. It was much easier to earn status with AA until they changed the program and now look at dollars spent instead of miles flown.
I only used Avios to book short OW Award flights (the last one was a JAL flight from Japan to South-Korea).
The IB account is because Iberia often sells Avios on Groupon. The first few times it was a very good deal but recent offers were much less interesting.
Last year I haven't been loyal at all (only one OW flight with British). I'm not sure what I will do in the future.
All my flights are leisure and I'm price-conscious, I will only book Business when it's a good deal. Redeemable miles earned on AA are peanuts but BA is not that much better in that regard. I think it's slightly easier to earn status with BA if you fly business.
As I'm based in Europe I think I can now get slightly more value from BA's program.
I used AA miles for long haul business flights which offered great value.
As it is much harder to collect miles with cheap economy flights I think I might be better of now collecting Avios and spending them on short Economy award flights.
That's my 5 cents based on what I know about the 2 programs. I didn't do an in-depth study and I must say I'm still in doubt (it's much more fun to use award miles for comfy lie-flat business seats) so I still want to do some more homework before I decide.