Welcome to FT, RTW1!

I am pretty sure you don't mean HON, you mean HNL, correct? Otherwise this would be an interesting surface segment.

This is a very nice routing and of course I would recommend using business class.

On that topic: be aware that SQ charges high surcharges to use their 77W and A380 business class so factor this in when planing your trip. Also, unless you find a NZ 777 flight to RAR you will be missing out on their great C product. It might make sense to almost skip Australia for this and fly AKL-HKG-LHR-DUS instead which would also solve the SQ surcharge problem.

And in terms of UA vs LH, UA now has the better hard product with a fully flat seat while the LH one is angled. The LH service will be better however. As it is a day flight the sleeping position is not that critical but you must decide how important that is.

Otherwise, SFO-LIH, HNL-AKL and RAR-SYD are operated by very ordinary business products.