Depending on where you live (and fly), BA can also be an interesting option, I was with them before switching to DL and the way status works is kind of similar to old Skymiles. Status is purely via flying, but with tier points based on distance and booking class per segment, so there's some interesting sweet spots in earning. Eg. premium economy often costs not much more than Y, but earns almost as many tier points as J. Similarly, putting in a connection on the east coast when flying Europe to west coast can almost double TPs.

Status gives you some very nice loung options across the OW alliance, no matter which OW carrier you fly with; especially nice if you frequently fly via LHR T3, which has QF and CX lounges. Avios redemptions tend to have some pretty steep taxes and surcharges, but (1) BA often releases all remaining seats for Avios bookings day of departure, so Avios can be a lifesaver for emergency travel, and (2) you can transfer Avios between BA,IB,EI,QR, so there is sometimes ways of booking the same flight with fewer surcharges.

All depends on your travel pattern, of course. If you frequently fly TATL, a stop in London probably doesn't make a big difference. If you fly between destinations in mainland Europe it's probably tough. Within the US, you get lounge access on AA even on domestic itineraries, but of course no complimentary upgrades.