Can't speak for the QF program, but BAEC does have its merits.

The distance-based award structure makes Avios unbeatable for short-haul redemptions, intra-European or US domestic on AA. Examples: LAX-HNL is 12,500 Avios but 22,500 AA miles. AUS-DFW or LAX-SFO is 4500 Avios compared to 12,500 AA miles.
UuA: Upgrade awards cost half the Avios compared to award tickets. An especially good value is upgrading revenue WT+ "T" fares (discount premium eco) to CW (business class). For around $1,400 (cost of "T" ticket) and 1,000 Avios (net cost - the upgrade requires 14,750 Avios but then this flight earns 13,375!) I can fly from here to LAX in business class. Doing the same thing with AA would cost about the same in cash ($1,000 discounted eco ticket plus $350 co-pay) plus a net cost of 13,000 AA miles (earning 12,000 miles, upgrade cost is 25,000), AND I sit in Y for the European leg.

BAEC's expiration policies are the most generous with any activity in three years.
And they offer household accounts where a family can pool their miles - great for travel with kids where you get to use their miles without transfer fees etc.

The truly savvy Oneworld traveler maximizes value out of different programs - and should always have some Avios handy
For example, I credit my shorthaul EU flights on AB metal to AB because the earn rates for discount economy on AA just sucks with 25%. AB gives me 100%. I credit most of my car rentals to BAEC, as I get 50 miles per day on AA but 500 Avios on BA when going with Avis.

There simply is not "the" best program out there in OW-land. AA is a very good one, for sure, but it's not necessarily 'the best' for everyone.

I signed up for the Plat Challenge today, and went into the Finnair website to change all of our FFPs to our AA accounts. But when I log into my AA account to search for my flights under "View Reservations" and further with "Find A Reservation" by putting in Carrier (BA), Flight Number (16), From (SYD) and Departure Date, I get an error message "We are unable to retrieve your reservation with the information provided".

Is this normal or is there something I need to do to get my flights showing up, or is it a matter of time (ie. wait a day or 2)? Curiously, my ORD flights are QF ticketed and even though I've got the corresponding AA Record Locator, and our AA# against the booking, it's also not showing up under "View Reservations" although I can search for it through "Find A Reservation".

I have tried searching on FT for an answer but can't seem to find one. Any help is greatly appreciated.

Can you find the BA16 reservation in the BA site ManagageMyBooking? Or even the QF web site?

I can on BA, when I sign into my BAEC account and all my BA flights are there. When I check them individually, they all show my AA#. The SYD-ORD flights can be found on QF's MMB, although when I log into my QFF account and click on "View Your Bookings", it doesn't show the flights. In MMB, the SYD-ORD flights also show my AA#.

That your flights are not showing in QF's MMB is to be expected since your QFF number is not associated with the booking

And I fully expect it not to, but what about the fact that none of them are showing up on my AA account when all the flights have had the AA# applied to them? Is it a matter of timing, given that I can still see them in my BAEC account?