The Fat Frank shares the same carcass, flat protection (kevlar belt) and rubber compound as the Big Apple. The only major difference is the retro look of the Fat Frank. The Big Apples might handle/grip a bit better as they likely put a little more rubber to the pavement. Beyond that they are very similar in their feel and performance.
Another option is the Big Apple Liteskin. It's a Big Apple with a folding bead, and the rubber compound is grippier.