FAT would be ever so slightly faster because of lower overhead, but it lacks the security and efficiency in terms of disk utilization that NTFS has.
So, unless you have some specific reason for using FAT, use NTFS.
BTW, FAT no more or less stable than NTFS. If anything, it's more stable, since the original, FAT12, was created way back when so that DOS could access floppy disks. Since then the basic structure of FAT hasn't changed, it's just been altered to be able to use larger and larger disks. NTFS didn't exist until NT came into being, and by that point, FAT had already been around for around 10 years. FAT is also far less complex than NTFS, since it doesn't support permissions like NTFS, and now NTFS also supports transparent compression and encryption, which FAT doesn't. Still, despite all that, NTFS is the better choice. Just wanted to correct the other responder, and was too lazy to make another post.