Are all iPhones the same across carriers now?
No. In the US, CDMA models can work on GSM but the other way, not so much.

Worse, in the US, Sprint and Verizon are not willing to bring aboard a device from the other carrier despite CDMA and GSM potentially being technically compatible.

The GSM phones when unlocked work across pretty much any GSM carrier.
The CDMA phones when unlocked also work across pretty much any GSM carrier or the specific carrier that the device was assigned to initially. (So I would generally be able to bring a Verizon iPhone from another person to my Verizon account)