iPods (except iPod touch) are simple media players, not computing devices (like an iPhone). There's nothing really to compare; when an iPod is not operating properly (after trying a simple restart), the next action is to do a Restore on it. This erases the iPod, reinstalls its software, and sets it to default settings. After doing a Restore, it is back to "factory" configuration, like when you took it out of the box. To make two iPods the same, do a Restore on both; then set up both to sync identically.
Here's how to do a Reset (restart) on the iPod
Learn how to reset your iPod - Apple Support
Here's how to d a Restore
Use iTunes on your Mac or PC to restore your iPhone, iPad, or iPod to factory settings - Apple Support
If you use Windows, one thing that may be different between two iPods that connect to the same PC is the assigned drive letter. On a Mac, two iPods should be treated by the Mac without distinction. But this is probably not relevant to this problem.
As the error message suggests, the problem seems to be in iTunes connecting to Nike+. Apple probably has not changed how it sends workout data to Nke+ in a long time (no need). However, the Nike+ website has been overhauled recently (at the same time this issue popped up). It's now completely different.
What's interesting is that my old ipod WILL still sync with no errors...
NOTE: That error message comes up ONLY when the iPod nano has new workout data. There is no error when doing a standard iTunes sync, because iTunes is not trying to connect to Nike+. So, if your new iPod nano does have new workout data (because you used it last for exercise), the error message comes up. If your old iPod nano has no new workout data, no error message.