Thanks for the clarification. I have hard time staying on top of such matters because the landscape changes so quickly. For example, UA killed this practice shortly after I abandoned them, and I think DL might have followed suit.

It's a silly practice when you think about it because award inventory often doesn't open up until the 3-day mark.

Conclusion:
-I still love AA miles
-BA miles are more useful for close-in bookings

And how do you exactly use BA miles on AA?
Now that I have gotten over 200K BA miles (Chase promotion), I looked at the BA.com for redemption availability and all it shows are BA flights. Considering that most of the connections require airport change LHR->LGW (where you have to drag your own language) and approx $400 in fees and taxes for a coach ticket, it does not seem like such a hot value.

Flight redemptions on the Thank You network have no fees. Plus you can earn FF miles on the flight.

You can book AA flights on ba.com or over the phone (ime they are often willing to waive the phone fee for flights that aren't possible to book online).

Setting aside the fact that TYN isn't really relevant to this discussion, they charge around $7 (in points) for airplane tickets (see below).

Expedia:

TYN:

This is true if you are looking at a route that BA flies, but if you select (for example) a domestic USA trip the website will show American and Alaska awards because BA does not offer service.

Bear in mind that BA miles cannot be used to fly on AA between the USA and the UK.

You cannot fly AA US-UK on BA miles - due to the government regulations the 2 programs initially agreed with decades ago the OneWorld alliance was formed. That is a limitation put by government on BA and AA. (the opposite is true for AA - cannot use AA miles to fly BA US-UK.)

Other than that, any OW partner flight is eligible for BA mile redemption.

I believe it is anywhere in Europe, not just the UK.

So, if I understand this correctly, I could use Finn-air or Iberia to travel to places in Europe (other than UK), provided I can find reward availability on those airlines. Right?
Now, for the fun part, where can I find the reward availability for those airlines? BA.com is not showing them.

Right. you can find availability is you search hard enough. Iberia has quite a high amount in redemption fees too. FinAir is pretty cheap, but if my memory is correct, they only fly into Finland.

You are right. It is no Transatlantic flight on AA, in the case of BA program.

However in the case of AA program, it is no US-UK flight on BA only. You certainly can fly Canada or Mexica to UK on BA using AA miles.

In other words, BA rules are more restrictive than AA rules in this regard.

Yes.
You need to check the box of searching partner flights in order for BA website to show you the availability on partner flights. It is on the left sidebar on one of those screens.

Also, BA program has separated Europe into 2 zones - therefore IB to MAD is in Europe 2, costing a bit more miles to UK which is in Europe 1. However, you may want to check with BAEC if you can still fly, say JFK-MAD-CDG for example and still be in the Europe 1 level.

Finally if you only use LHR as a connection, you can avoid the notorious APD LHR charges. Check out Steve in Olympia's posts on his SEA-LHR-GVA routing - only costed him $288 for a r/t award.

But you can then fly AY from HEL to other location in Europe, on the same award. You dont need to have HEL as your destination.