Which password? If it's encrypted, you'll need the backup encryption password. In my case it's automatic. I see it filled in as hidden characters and I just press enter. I've recovered from the backup several times.
If you can't figure it out, you can perform a new backup, but make sure to reset the settings to default on the older iPhone, which will allow you to create a backup that's unencrypted (won't copy over saved passwords) or to choose a new encryption password (will allow copying over of saved passwords). Just Settings > General > Transfer or Reset iPhone > Reset. This is NOT "Erase All Content", which is obviously what you don't want to do.
Return iPhone settings to their defaults - Apple Support
Other than that, you might try erasing your new iPhone and get it back in factory settings, then when it comes up use Quick Start to perform the transfer. It's a little bit different and transfers via Bluetooth. It also uses the camera to sense a moving pattern.
Use Quick Start to transfer data to a new iPhone, iPad, or iPod touch - Apple Support