I've been on the LHR-SIN route with QF and BA in PE/WT+. I think the QF's PE product is much better than BA's. As you'll find in other threads on the topic, BA is essentially a Y+ plus product and QF's PE is more like a J-.

The seats themselves aren't that different from BA's. But you do get pre-takeoff drinks (including cheap champagne), better presentation (tablecloth, etc) and better knives n folks.

Food... I've only flown one flight on QF's PE, but it was not your average Y class grub - it was much better than BA's WT+. But that is my own limited experience.

I think the QF hard product is better but I got irritated at being called a "mate". ;-)

Personally I would go for QF over BA for the premium economy product but the price premium that it often attracts is a little bit much, but occasionally it does match BA's own as that's how I managed to bag that flight way back in January.