Fortunately most of my RTWs are in F. I tried a few airlines in C in the last year or so.
I really liked the new C on SQ (340, 777, 380 - i know, not Oneworld). Air NZ was also pretty good for sleeping and had good privacy when travelling alone. I cannot sleep well in the slope style lay flat (LH, old LX, AA, QF). BA is too cramped for me. Cannot say much about the new CX (F is great).
Look also at the Star RTW or some LHR-AKL return fares (potentially with some extra side trips from HKG and/or LAX) on NZ.