You seem to be comparing the redemption table of AAs scheme FOR FLIGTHS ON AA ONLY with the BAEC redemption table for FLIGHTS WITH BA.

AND:
You fly from YUL (i.e. Montreal-Canada).
You are looking at costs to Japan (by the looks of the AA table 2x50k=100k)

THEREFORE, a BA flight from Canada to Asia will go via London (i.e. two continental jumps). An AA flight will go direct (continent to continent).

A BA miles redemption on the metal of A SINGLE PARTNER only (i.e. to fly AA on the same flights AA would put you on) costs 50k return in economy. 2x50k=100k return in business for your origin and destination. See link below. [Japan is in FAR EAST category.]

There are PLENTY more factors and things to think about, especially since you would be based very close to the home of one scheme (AA), and not close to home base in the other (BA).

So, I'm not trying to tell you which to take, nor am I trying to tell you it doesn't matter, all I'm saying is you were not comparing like with like!

https://www.britishairways.com/trave...club/_gf/en_ca

[Hope my CAPS didn't sound like shouting, flu'd up here - hard to judge how it comes accross!]