The AmigaOne (and Pegasos) have no relation at all to the classic Amiga hardware. There isn't a 68k processor (they're PPC based) and no custom hardware.
AmigaOS4 is the first version of AmigaOS that will run natively on the AmigaOne board. The idea is to leave the old Commodore hardware behind, but that also means compatibility with some programs will be broken.
I think you'll need a Catweasel to read old Amiga floppies on any machine that doesn't have the old custom chipset.
