The 1600 AF (the one with the smaller Wraith Stealth cooler) is actually a slightly underclocked 2600, so I believe the board will need Ryzen 2000-series support. I suspect any A320 board should have a BIOS update available to enable that, but A320 boards manufactured before the 2000-series came out may not have that installed from the factory, whereas B450 boards definitely will. If you are buying one in a physical store, boards shipping with support for those processors are likely to have a "Ryzen 2000 Ready" label on the box, though from online stores it might not not be as clear. I'm not actually too certain on what the situation is like for Ryzen 2000 support on A320 boards at this point though. It may be that most of the boards include 2000-series support from the factory now, but I can't say for sure, as there may still be some old stock floating around.
If required, it's possible to update the BIOS on your own, but you'll need to have access to a compatible 1000-series CPU to perform the update with. I know AMD had a program for getting a temporary loner CPU sent to you for that purpose, and I think they still do, but that might potentially delay your build by a couple weeks. If you buy from a physical computer store, they might be able to do that for you too. In any case, if you go A320, it might be worth verifying that the board in question comes with 2000-series support out of the box.
Hardware-wise, aside from overclocking support, the differences mostly come down to connectivity, but that may not be much of a concern on an ITX board. B450 makes a couple more PCIe lanes available for example, but an ITX board isn't going to have more than one PCIe x16 slot anyway. It's also more likely that a B450 board may offer a better power delivery system, but that can vary depending on the board, and is only likely to be a concern with the higher-end processors that can draw more power, and at stock clocks, the power draw of just about any Ryzen desktop processor should be pretty reasonable, so again, it might not be too much of a concern.
One concern I would have would be support for newer processors, should you ever decide to upgrade your CPU to a Ryzen 3000 or future 4000 model down the line. Some A320 boards offer 3000-series support, but its not guaranteed, whereas all B450 boards should support at least the 3000-series with a BIOS update. That's something you might want to check on the manufacturer's site for the specific board you are looking at. Looking at the support page for the least-expensive A320 ITX board at Australian online stores on PCPartPicker, the the ASUS Prime A320I-K, it does look like that processor may have 3rd gen Ryzen support with a BIOS update, so that might not be a problem either.
Considering the price difference on the models you are seeing, A320 might be alright for an ITX build. The 1600 AF is clocked reasonably enough out of the box, so overclocking might not be too important.
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