I've had pleasant experiences on both, with surprisingly good and attentive service. In terms of differences, YMMV, but from my most recent experiences:
- Depending on the aircraft, WTP cabins can feel quite dated, with dirty surfaces and antiquated IFE. AA's hard product is far superior.
- The food on both is fine - equivalent of a domestic First meal, though I'd say AA's second meal offerings are far superior than BA's.
- You'll get a PDB (champagne, water, OJ) on WTP, nothing on AA (that's the policy, not a service failure).
- Although I don't know for certain, I got the impression that WTP has one or more dedicated FAs. AA's PE does not.
- If you're the type of person who cares about these things, BA uses glassware for wine in WTP; AA uses plastic (like DL and UA, I believe).