Purely thinking transatlantically, in terms of UA vs AA

UA: travel on UA, US, CO, LH, SN, LX, AC, OS, TK, SK, LO, VS
AA: travel on AA, BA, AY, AB, IB, EY, TN

Now, using UA miles, you can mix and match partners at will, and most partners in that list (with the exception of US and LX, IME) have great award space. No fuel surcharges.

Using AA miles, you have the insane published fare rule (which significantly limits potential routings on AB/EY/TN). IB's product is horrible, and BA has insane fuel surcharges. This essentially leaves AY with bad award space, or AA's own metal (whose product isn't too flash anyway). Hmm...

As to the subject of ultra-short haul rewards, LAN is a lot better than BA in every regard- transfer from SPG at a 2:5 ratio with the shortest awards available for only 6000 LAN km's (2400 SPG points!). In my eyes, BA Avios points are more or less in the same category as Qantas Frequent Flyer points- worthless.