No need to switch programs if you fly within the alliance. One World options include QF, CX, JL & QR. I'm not a huge BA fan so not going to argue you there. My favor would go to CX & QR on the LHR-SYD routes. QR economy on their A380 is pretty good and way better than BA's 777s. Downside is no PE like on CX, BA & QF.
BA Avios can be a great value for flights within Europe as it is distance based but can also be a poor value since revenue ticket prices can either be very cheap on BA or via an LCC. Avios also tend to be quite a good value for CX redemptions.