Difference between iPod 5th Generation (80GB, late 2006) and an iPod Classic (160GB, late 2009)?
Well, of course there are differences. :)

However, the only difference I can see that may impact your usage is that the latest version of the OS that will run on these iPods is different. The 160GB iPod can run up to version 2.0.5 of the OS while the 80GB iPod can only run up to version 1.3. So I suspect your issue may have something to do with what the OS supports.

In terms of the USB connectivity via the built-in 30 pin port, they both support USB 2 high power charging, so it's not likely to be a physical port issue.

You could probably find a different 30-pin to USB adapter that will work for the 160GB iPod for input to the receiver in the BMW, but that may involve a fair bit of trial and error.