Aside from certain situations where you’re taking pictures and the use of the always on display, there’s no difference. The molar reasonable thing to do would’ve been replaced the battery on the 13 for $99 and then wait another year or two for an upgrade.
I don’t know about the iPhone 12, but on the iPhone 11 there’s a dual purpose antenna that connects directly to the motherboard that snaps into place was that properly reinstalled in your phone?