A bit of googling turned up this page:
Its a bit out of date, but it describes the main issues. Main points are:
1: ext2 used to have a 2Gb limit, but not any more. The limit is now 2^63 bytes.
2: Applications need to be recompiled (and maybe modified) to use 64 bit file index and size data types.
3: There is indeed a 4Gb limit on older versions of the SMB protocols. Ahem. This is rather embarassing, since it answers my original question. I did find this page when searching earlier, but failed to scroll down far enough to find the list of file systems and their limits.
So now I'm going to have to do work-arounds. I guess I'll use MS backup for C:\Windows and smbtar for everything else.