Restoring new phone from a backup of a different phone

I recently upgraded to a new phone. While the setup for the phone does have some advanced abilities to transfer from my old to new, I couldn't restore from a backup from my SE. The error message said that my phone was locked, and I needed to enter the code. When I started the backup, it was not locked, and my passcode was not requested. Instead, when my phone began backing up, the screen locked itself and had on the screen "restore in progress," which I assume is a safety feature to properly process the restoration. I go through the restore, my phone restarts, and then I get the error I mentioned above. I would like to avoid a factory reset and redo the setup if at all possible. I have also tried uninstalling and reinstalling itunes, restarting my computer, restarting my iphone, and nothing helps. There are no other issues with connecting to itunes, and I can make a backup from the new phone without a hitch.