Is there any advantage in formatting my iPod Classic one way or the other?
The only advantage I know is that FAT32 is visible on both windows and Mac
But, is HFS is better performances wise?
As far as I know, Apple designed the iPod to work as FAT32. While it will work as HFS/HFS+, I don't see any reason for it to work any better or have performance boosts from being formatted differently.
I have a 80 gig 5th generation Classic that I formatted with HFS purely because I use it as an external drive, and the maximum filesize on FAT32 is 4 gigs. My primary listening iPod, a 7th gen 160 gig Classic, is on FAT32. I haven't noticed any difference performance-wise between the two.
At the speeds you are playing audio off the media, there isn't going to be any significant difference between FAT and HFS (or ext4, or...). You may see a significant improvement with a more modern filesystem than FAT when copying large amounts of data to or from the drive.
Edit -- The file-size limit on FAT is unlikely to impact you for music unless you are using tar or the like to create large archives. Video may push it.