The first difference I noticed is in System Update. The version running showing actually now indicates Android 13 instead of Android 12, which it did even though the phone is on A13 Beta.
A new and useful feature in Android 13 Beta that I really like is the "Copy, Edit then Paste/Save" feature (not sure what to call it). I've used this feature many times to copy some text or URL, add my comments to it, save it, and then paste it in a thread, Twitter post, etc.
I checked my wife's Pixel 4a on Android 12 and that feature doesn't appear to be on her phone.