Another aspect might include EU261 regulations applying both ways on the European flights if booked on BA vs only out of Europe if booked on AA.

When I flew a mixed itinerary last year. I was able to enter my AA PNR on the BA website and then it kicked back the page with my BA PNR, only updating the PNR in the form I submitted, and I had to reenter all my passenger information.

EC261 would not be affectef by where the ticket was purchased not whether it was a codeshare or not

Flying on AA metal into the UK is not covered, but is covered flying from the UK. Flying on BA metal would be covered both ways, though I’m sure I read about a court case when a claim was thrown out because of the fact that even they were on a BA flight flying to the EU, as it was on an AA ticket, so not covered.

That wasn't my point - Indeed I know that AA US->UK is not covered. My inferrence of the OP is that the same actual operating flights would be purchased - the only difference would be where they were purchased ( and potentially may have been a codeshare )

It doesn't matter where they were purchased nor whether they are codeshares , EC261 protections will be identical

I've had tickets JFK-LHR (aa metal) + LHR-ZRH (BA), purchased on www.aa.com. When I went to www.ba.com and entered my AA PNR, ba.com found me and I got ba's PNR--all without "human" intervention.

It works in the other direction too. BA-ticketed, AA-operated flights will additionally show AA's PNR in Manage My Booking and seat selection redirects to AA's website.

As alluded to above, if ticketed on BA, AAdvantage points will be awarded based upon a factor of the miles flown, whereas if AA-ticketed it will be a factor of the dollars paid, if you're bothered about such things at this time.

Thanks again very much for the useful replies. She made it home, though in the end did not book the AA/BA flight. But I very much appreciate the help.