Just returned after living in Oz for 9 years....so am familiar with that route...If you travel BA, they code-share with Qantas so you could end up on a Qantas plane or vica verca....For service, I'd definitely go with Singapore if their prices are competitive. If you have a choice transit through Singapore as opposed to Bangkok. Lovely airport where you can have a shower and a few relaxing hours as opposed to Bangkok where its smelly, too small and the amenities are very average! Have a great trip! Oz is a brilliant place to visit!