I've said multiple times over the course of these forums, but I'd like to see chocobo jousting. I've thought about it a lot and I think it could work something like this: your Grand Company chocobo can also be used in tournaments for the glory of your company. Although not hostile to each other, the chocobo jousts are the perfect solution to entertain the denizens of Eorzea, as well as drum up support for the Grand Companies. By earning chocobo company credits that you win against another company, you could then use them to upgrade your bird, buying armor and the like. The match itself could just be a simple rock, paper, scissors where you tilt, defend, or shift against an opponent. Perhaps over the course of upgrading your armor, your chocobo can sustain more hits, so instead of going best out of three, your able to go best out of five (provided you don't win the first three).
Uh...sorry if that got a bit off from your topic. To tie in to your suggestion, perhaps the armor you could earn would have different abilities that function outside of the joust, such as increased speed and defense in the field, according to the three archetypes you've designed, further increasing the differences of the Grand Companies.