Join Date: May 2012
Location: Munich, Algarve, Sussex or S.F Bay Area
Programs: Mucci, BA Gold, A3*Gold, AA Plat, HH Gold, IHG Plat Amb, Marriott Plat
Posts: 4,158
You are going to get jetlag, that is for sure. My personal take on it is that I'd rather get to my destination as soon as possible and acclimatise there rather than get the first hit of Jetlag in, say SIN, and then a second hit in SYD. Both flights are overnight if you stick to BA the whole way.
As for PE vs. CW I cannot say, but reward space on LHR-SIN-SYD is quite rare, so if that is not available and work only allows PE then you do not really have too many options apart from perhaps choosing Cathay PE via HKG rather than BA via SIN. By all accounts it is a nicer product, although I have not experienced it myself.
You might like to book BA and hope that CW upgrades open up closer to departure date. This has been my experience, but the route is usually quite busy and I am not sure how likely that is.