We've been to most of the Bali FS and Aman properties and wrote up a very detailed trip report on this forum. I highly recommend that you do a search for it...it's a few years old but there's lots of good info comparing the properties.
If we could do it all over again, we'd go all Aman. The trip report explains why. If you are really anxious to try both brands while there, I'd recommend FS Sayan and Amankila (in that order).
Ericka