The hunters will be larger and better equipped than the Hobart's. It's irrelevant whether we call them destroyers or frigates.
I certainly don't think there is a considerable amount of difference in terms of original capability between the two. The Hobarts will appear to be more tightly integrated with Spy + Aegis and a larger vls magazine, making them more suitable for Aegis fleet integration and possibly for SM-3, as well a larger missile load out enabling things like tomahawk. The the difference is mild out of the box, the Hunters have much more room for growth and will probably have a deeper radar horizon and would likely make better ships for individual work.
But I think people are missing what the current ADF and Australian defence discussion is.
It is more about Australia not having a navy at all. Its more like stop building Hunters, get rid of the Hobarts, push the SSN acquisition way, way into the future (shelved). Buy B21's. Perhaps build patrol boats.
It is not a continuum between new Hobarts and Hunters. Its effectively removing large area defence vessels from the RAN, the big ships. Removing both Hobarts and Hunters from the future (or curtailing their build at 3-6). Replacing them with aircraft. Building more Hobarts will be an argument for more Hunters, not the other way around. This would also include disposing of the LHD's and going with smaller amphibious ships that do not need escorts (or so the logic goes). Basically break the submarine arm as well, it turns out SSN's are hard and expensive. Hard to build, hard to operate, hard to dispose of. The USN isn't going to base 12 SSN's and 2 SSBN in Australia. They aren't going to pay for upgrades to FBE and FBW.
Osborne and henderson can then build small ships <2000t. These would then adopt the ASPI Patrol boat battleship concept of putting a NSM on them, maybe with a 40mm gun to deal with air threats. These ships would operate in Australian waters under the safe protection of the RAAF.
This then frees up lots of money for aircraft.
The argument goes that aircraft are more flexible, faster to respond, more survivable. Western doctrine generally has aircraft as the tool for anti-shipping, not ships, therefore, pointless to build large ships as in future wars they are too open to attack, and Australia needs to focus on sinking chinese naval assets. The US is basing B-52's here and will likely base B21's here. So Australia will defund its Navy to fund a much more capable airforce, based around long range bombers. Which will be based up north. The US has already funded upgrades to Tindal.
Also, it is argued it is too hard to staff and crew the Navy. Australians would prefer jobs in the air force. Therefore we should abandon these hard to staff platforms. Fund more upgrades to airbases and long range strike platforms.
I would be interested in how people see that proposal working. Particularly we would be basically be abandoning or winding up any existing ship acquisitions right now, and B21's might appear sometime mid/late 2030's. Perhaps.
I think there is more to defence of Australia than bombing mainland china with B21's. Which likely won't be survivable in Chinese airspace in 2030.
I am also not convinced that moving the Australian navy into a brown water force will solve our problems, nor will again abandoning local manufacturing of complicated things like ships and land platforms for a US off the shelf wonder weapon.