Certainly on the domestic end MEL has better QF lounges. International, I will concede that the J lounge leaves a little bit to be desired. EK lounge at MEL I will concede I haven't been to but if it's anything like the SYD one it will blow the QF International J lounges at any Australian port out of the water.
Between the two Centurion lounges SYD and MEL, the MEL one is slightly better as they have those nice little suite things like they have at LAX. Unsure about the invite thing you are talking about, just flash your Platinum card and they'll let you in.
If you are departing around when the EK lounge is open and you are travelling on a QF/EK flight anywhere except the Americas it can be quite good. Here's some shots from the SYD EK lounge when I was flying QF Y over to CHC back in December:
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