I have flown on the new QF seats yet, but have loved my flights on BA when I was able to get business seats. I always go for a window, which is rear facing and the most private seats on the plane.
I prefer upper deck windows as this gives you a little locker between you seat and the window - perfect for storing stuff that normally ends up on the floor, as well as laptops, etc.
IF you are one of the lucky ones (like me) that has sleep apnea you'll be able to get authorisation to plug in approved apaps/autopaps on QF, but you need to do this a few weeks before flying. It's OK on BA, but you need a special power inverter that they sell on board for 75 pounds.
Personally I would do something like MEL-SIN on QF and then BA to LHR. You should be getting 4 stops once you land in Asia so why not throw in a few spots (HKG, BKK) along the way? You'll get more FF miles!