Quickstatus, a definitive measure is through
FlightStats - Global Flight Tracker, Status Tracking and Airport Information and anyone is best to look that up but my sense is in summary, and subject to variation on a daily basis for QF (not JQ) medium and long haul flights - simply a broad 'back of the envelope' guide. Where I have not stated otherwise, my assessment is for all routes, both directions operated by QF ex and to Oz.
Excellent punctuality: Oz to and from Dallas Fort Worth, Japan flights and most often Bangkok, Jakarta, Hawaii and Shanghai with Sydney, Brisbane or Perth to Singapore and Brisbane to Hong Kong also featuring. Japan is probably the standout with the Brisbane and Sydney to Narita and Haneda respectively flights hardly ever late in either direction, notwithstanding that occasionally due to the much featured B744 problems on earlier pages of this thread there have been up to 24 hour occasional delays with the Sydney - Haneda flights.
Very good punctuality: Brisbane to Los Angeles (but not always the 'tag flight' on to New York, sometimes due to extremely difficult weather), Johannesburg and (seasonal) Vancouver (note: at times it would be fair to place all three in the 'excellent' category).
Very good punctuality but subject to airport or airspace congestion delays at the Asian end: Manila
Fair punctuality: Melbourne or Sydney to Hong Kong, Sydney to London and return, San Francisco, Santiago and Melbourne to Singapore (note: Hong Kong and San Fran can often be 'very good' but in the last couple of months there have been a couple of bad delays if I recall, so they are marked down a bit for that)
Due to the extra padding QF introduced for the northern winter QF1/2/9 and 10 timetables between Oz and DXB/ LHR and return, even the SYD flights may sometimes be less late arriving LHR than they were arriving in DXB provided the airline is able to adhere to the allowed time for the intermediate stop, as the second sector has a particularly slow timetable now, allowing time to be often picked up.
The padding has ensured that SQ's flights are now the fastest option for travellers - and that airline tends to have superior punctuality and reliability compared to QF.
Poor punctuality: Sydney or Melbourne to Los Angeles or return (sometimes due to the late running connection from New York if westbound), Oz to or from New York
Appalling punctuality: QF9 and QF10 Melbourne to Dubai and London and return - use a reliable airline like SQ with better frequencies and a more pleasant route via the best airport in the world in Changi instead!
I have omitted shorter routes such as New Zealand and closer Pacific destinations but flights to and from NZ can have wide variations in punctuality, perhaps a tad surprising.
My suggestion is that BNE has more punctual QFi flights overall than MEL, again surprising because neither are at the undoubted core of QFi's network which remains SYD and hence if planes are defective in either BNE or MEL, replacement 'ferry flights' such as QF60XX may have to operate should a spare be available, so one might think that punctuality and reliability would be roughly equal at BNE and MEL. Of course MEL has QF9 and 10 which bias the figures as adverse for MEL; BNE has no such equivalent long haul QF flight to or from Europe.
I hope others see this as a fair assessment, but obviously on any one day things can be close to perfect, or one or two flights or the whole network can be in chaos.