I cannot speak for BA Premium Economy, but I just flew JAL PE from Los Angeles to Bangkok. The shell style seat was not very comfortable in my opinion for such a long flight. I was never able to sleep. Not a lot of cushion. The meals were exactly the same as economy. Not bad but nothing special at all. I was not impressed at all with the inflight entertainment system. Very few movies or TV shows. Seems like an outdated system. I'm comparing the JAL IFE system to Alaska, American, Cathay Pacific and Singapore which have hundreds of selections. The Sapporo Lounges in NRT and BKK were packed with people and besides getting a something to drink, was not really worth hanging out in.
In all fairness, the JAL flight crews were excellent.
I am flying BA PE in December (PDX to LHR) segment and Singapore Airlines PE (LAX to SIN) segment in October. I will post my experiences on each trip flying in PE.