I'm a little surprised this is such a crucial feature for you. Personally, I've never noticed refresh rates that aren't below 60 Hz but I get how one's eye gets used to the better quality. For me, iPhone 13 would need some UX changes, phone book contact management being a crucial one. It'd really be nice to have a more streamlined experience.
Fortunately for Apple, Samsung has begun worsening their flagship phones. The Galaxy S21 dropped the MicroSD Card Slot and dropped Magnetic Secure Technology (MST) for Samsung Pay.
MST is extremely useful in the United States, and some other countries, where many merchants don't yet accept Apple Pay or Google Pay with NFC. I use MST on my Samsung Galaxy Note 9 at least a couple of times per week. When a merchant sees me holding my phone by the payment terminal they will often say "we only take Samsung Pay" while they used to say "we don't take Apple Pay." I am definitely not going to "upgrade" to a Samsung phone that has dropped MST.
If the iPhone 13 brings back Touch ID, goes to a 120Hz display, and improves the cameras, it will be as good as the Samsung Galaxy S21. I would definitely not buy an iPhone that lacks TouchID, though a 120Hz display is not a necessity for me.
It's kind of ironic that Apple may catch up with Samsung as a result of Samsung removing features from its phones, while Apple adds features that Samsung has had for two years. It's also ironic that some of Samsung's new mid-range phones (the A series) continue to offer both MST and a MicroSD card slot, though with only a 90Hz display.