I am probably in a different situation than OP's friend but I found that combination of UA for *A and BA for OW works best for me. The reasons are the following:

• I mostly travel US domestically and TATL (some intra-Europe). It is good to have a status on a US airline for domestic upgrades, IRROPs, etc - US airlines are notorious for treating their own elite customers better than non-elites paying premium fares. On the other hand BA allows relatively cheap and easy redemptions on TATL and European routes, unlimited upgrades to business class for just 12500 miles one-way from any WT+ fare including deeply discounted (not 8 or 6 SWU/EVIP) and lounge access when in US (I even can use BA lounge in two of UA hubs: IAD and DEN when flying UA).
  
• I contemplated AA + LH combination but while AA in my experience superior to UA LH program is much inferior to BA, especially when flying in US. Here are some drawbacks:
  • Much more expensive upgrades on LH compared to BA
  • Elite levels structure works better for me on BA. I am BA Gold but I would never make LH HON (or BA Premier) and LH Senator is closer to BA Silver than Gold.
  • BA has very reasonable discounted business class fares out of London that I often take advantage of, e.g. flying UA to London and continuing from there. LH does not have this policy. (Though I must admit LX has and I might look into it in future.)
  • Domestically AA treats OW emeralds much better than UA treats *G.
  • Access to Admirals clubs (and AA IFL in a couple of cities they exist) is nice, though secondary. Access to RCC, and even without drink chits - not a huge benefit IMO. I usually call 1K line anyway in case of IRROP on UA.