I will soon be booking a Dublin to LAS/PHX trip. My issue is not with baggage or dropping the last connection etc as I want to stay in Dublin prior to see relatives and have no issue about going through Dublin on way back.

My question is 2 parts but related:

Is it best to book thru AA or BA? I am BAEC bronze having just lost silver, so want to make sure there is no potential loss of Avios or TP's.

Assuming no Avios/TP issues, does booking thru AA allow me to get free seat selection when booking or do I steel need to pay? (I am aware I get free selection on BA 1 week prior to departure).

Thanks in advance, apologies if this is covered somewhere else but I couldn't find anything specifically relating to this.