Others have fully answered the question about rotation and winds if your question was about the speed of the airplane. But if you want a practical answer about the trip time, what’s faster will always be determined by the available flight routes. For London to Sydney this will always be East, since connecting through the Middle East or Asia is simply a shorter trip.
http://www.gcmap.com/mapui?P=lhr-sin-syd;lhr-yvr-syd;lhr-lax-syd;lhr-dxb-syd
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