No Australia-specific documented benefits that I'm aware of. Undocumented - sure, QF are more likely to look after their own on their own metal, much as every other carrier does - so if most of your flights are in the US/UK, you won't benefit from that so much.

You're already aware of the 4 sector rule, so no need to cover that ground again.

When travelling on AA as a Gold/Platinum QF, you're entitled to Admirals Lounge access + drinks chits. I've not flown on BA metal, so I don't know what to expect there - but I'd imagine you'd get the documented OWS/OWE bennies at the very least.