The biggest diference is exFAT can handle files larger then 4GB in size.
FAT (as it is called on OS X but really FAT32) can only save files smaller then that 4GBs.
So if you don't need to save files bigger then 4GBs then you may want to use FAT32.
But if you do have files (Not folders, just files) bigger then 4GBs then you will need to use exFAT. But there is a caveat to using exFAT. Do Not use Mac OS X to format a drive exFAT, even though it is an option in Disk Utility. OS X screws up the exFAT format to the point No Windows PC will be able to read the drive. In fact when connecting a OS X formatted exFAT drive to a Win PC the Win PC will state the drive needs to initialized.
So always use a Win PC to format the drive to exFAT. It will then be seen by both Windows and Mac OS X.
There is another option and that is to use a program that can make either Windows or OS X read the others native format. But I do not suggest that as those program can, and do, screw up which could make the drive inaccessible to either system. Which would mean you would lose all the data on that drive.
Thanks for your swift reply, what's the difference between the two and which is better.