Could it be the thumb drive? I didn’t give it any thought when I purchased, so the drive is USB 3 whereas the old Mac would be USB 2
USB 3 shouldn't matter, because it's backwards compatible with USB 2, i.e. it'll work, but with USB 2 limitations.
As long as you're working with at least a 14 GB (as per Apple) thumb drive, I'm not aware of any reasons why you should be having problems. But then again, I've never been through the process and am not aware of its possible nuances.
