Nutty Knights to me seem more powerful than Fabulous FIDEs, but the known theory of the FIDEs and the unfamiliarity of the Charging mechanic makes the Nutty Knights complicated. Also, Fibnifs should stronger than Knights.
Players well experienced with Chess with Different Armies are likely Nutty Knights preferable, but players new to Chess with Different Armies would probably prefer the Fabulous FIDEs. This seems to be the case with the Clobberers and the Rookies as well, to a lesser extent.
One thing I don't get though, is why would Charging Rooks be a miniscule amount stronger than normal ones?