The point I would make here is that if the flights were operated by AA, it would be an absolute no-brainer to book with AA as there really is no advantage to booking BA for £15 more.

But as manord says, if both are op by BA, then there is some value in booking through the operator even if slightly more, as it makes it easier to handle if there are any issues.

As a side note, both AA and BA operate the LAX-LHR route. In Y I prefer to pick an AA op flight where there's a choice so I can pick MCE seats. The trade-off, in that direction, is no EC261 protection. If OP is booking the BA op flight anyway (and is in WTP) then not relevant in this case.