.17 Rem. a few hundred FPS faster....burns more powder and I believe is a 223 casing necked down.....17 FB right around 3800-4000FPS depending on ammo choice....burns less powder...a little less recoil and noise. Never shot the 17 Rem. myself. But supposed to be an excellent coyote gun. alot of guys on here use the FB and love it....I have shot them and don't own one....yet. That would b my choice since I primarily hunt fox and on occasion see a yote. Hope this helps some. I am sure you will get more answers from the guys that know a little more detail.
The way I look at it, they are pretty close, I would go with the extra fps. and the remington if they both come in the same rifle and it is one you like. Unless the fireball comes in a rifle model you like better that the remington doesnt come in. Then you are losing very little in the way of performance, in a rifle you will like better.
I have shot both. I noticed little difference in sound or muzzleblast. And neither have any recoil at all.
Either one will make a great fox/coon/coyote fur rifle.