Sorry it has been asked many times before but I am having real difficulties deciding which of the two programmes to use. I currently have a household account with BA exec (got bumped down to Bronze

I am based in London. My year looks approx. like this:

3 transatlantic flights to the US (economy)
10 flights US domestic (economy)
2 flights to asia (sometimes business, sometimes economy)
1 flight to Australia (business)
20-30 flights within EU (economy)

I like to travel BA.
Rest of family (2 people): 1 flight to Asia each (economy) and under 10 flights each within Europe (economy).

Which programme would be best for me to maximise value? My priorities would be to be able to upgrade to business with miles (or use miles to purchase flights) and access to a lounge.

I find it very difficult to understand the Aadvantage programme and found BA exec always very user-friendly and the website is a pleasure to navigate. However it seems much easier to attain decent status with aadvantage and get transatlantic upgrades. Is this right?
Should I continue to stick with BA in that case?