I’m pricing up an ex-EU hop across the Atlantic and the best option is coming up as all segments on American metal (though some have BA code share). Google Flights says I have to call BA to book as can’t do it online (presumably because some segments don’t have BA code share).

It'll cost me £35 to book by phone I think. But then I wonder - should I just book it on AA website? In general is there any benefit or negative to booking through an airline site other than BA (which is my loyalty program)?

Thanks in advance for any insights.