I have been doing a lot of research into BA's programme (as I now live in the UK) and it really doesn't stand up to much scrutiny.
You need far more miles to fly to other places, e.g 120,000 from LHR - MEL in J using AA or 200,000 using BA miles on the same carriers.
Also the top status benefits only give you 1 upgrade certificate for 2 people. You get further "pairs" of upgrades as you clock up more miles.

I have heard however, that they do op-up people in their 'club'.

Having said all that I was op-upped to A seat when flying J as an AA EXP on a flight from YYZ - LHR last year. It wasn't a real op-up, just the seat, not the service. Still J class service but bigger seat.

Of course if you do the pond trip often, the BA J class seat vs. AA J - no contest.