It's an interesting question, I guess. RAAF has a maximum of 57 "HUG Bugs" operational at any one time. More could be pressed into service in an absolute necessity with 2 Operational Conversion Unit being made operation with it's 10 or so bugs.
The 6x Wedgetails RAAF is getting should be far superior to E-2C Hawkeye in capability, as Hawkeye 2000 was one of the options looked at for the RAAF AWACS capability, and rejected as not being sufficiently capable.
With the 5x A330 tankers, our A2A refuelling capacity will be the best it's ever been, however that's not saying much, it'll still be "thin" at best. Another 3-5 would be necessary to ensure a really robust capability.
Our 19x AP-3C Orions are significantly more capable in the MPA and ASW roles than the Viking I should think and vastly outnumber that carred by a single carrier, and there's no reason our SeaHawk, would be any less capable than the US's.
In A2A roles, we operate the latest model AMRAAM missiles and the RAAF rates the AIM-132 ASRAAM as superior to the AIM-9X when they evaluated these for their new WVR missile requirement. However I don't think AIM-9X is operational in the USN (still using AIM-9M I believe), whereas ASRAAM has been operational in the RAAF since 2004. ASRAAM is most definitely superior to AIM-9M, so RAAF has a slight edge there.
RAAF is to operate JASSM, which it rated as superior to SLAM-ER, plus JDAM which is operated by the USN. RAAF does not operate a dedicated SEAD capability or a dedicated EA capability, so is quite a bit behind there.
I'd say, considering ALL the available assets, the entire RAAF could muster just a bit more capability than a single US carrier, but not by much.
Pretty ordinary really, in that light...