Ah, upon checking the book at home, any chocobo is capable of winning at fal'Cie level if properly developed, but Silver Chocobo is the most cost-effective of the lot of them. It'll be interesting to see which ends up best overall, if there is a 'best', that is - perhaps the Golden Chocobo? Dunno. But I'm kinda hoping to have a maxed out chocobo of a number of types, so I should be able to check it out.

EDIT: Never mind. Speed and stamina are capped at 800 strength/magic respectively. Anything above that will have no additional bonus. That explains why they suggest the Silver Chocobo route.