To clarify on Healer vs Free Stance, my choco is only rank 7 at this point, but I have had to use Healer stance on a few occasions. And to clarify, this is for a healer chocobo. I do not have any other abilities other than healer unlocked, so I can't comment on how the choco will react.
The primary significant factor is your chocobo will stop attacking on Healer stance. It is a healer, and will only heal at this point. It will cure you (the party) as fast as it can. It will keep regen up at all times, and it will follow you. The reason to note this is, if you switch him to healer stance, remember to put him back on free stance when you want him to attack again, otherwise he will just sit there and heal you (I have had a few times where I get annoyed with my damage sucking, only to realize my chocobo was still on Healer from some time previous).
On Free Stance it will engage the enemy the moment you do, and only the mob you target for engagement (I use this for flash if I don't want to pick a target yet, I can flash, and my chocobo will not attack, though he does start doing the pee-pee dance saying something is attacking me, and he wants to kill it).
On Free Stance, he will continue to attack the mob he starts on until it dies, or you tell him otherwise. This you do have to be careful with if you run into things you don't care to kill. As once he starts attacking it, he will not forget. So, let say, you switch him to a new mob. Once that mob dies, he will run back and continue on the previous mob, even if that mob de-aggroed and is just minding his own business now. They fixed most of the issues with this, but, you can still get your chocobo to run off and fight random stuff, if you get too bossy.
On Free Stance, a healer chocobo will throw out regens if the party is hurt, but will not cure unless your HP drops below 75%. Even then, he really doesn't care too much, and will only hit you with a cure about every 10-20 seconds (I haven't timed it, but if you are getting railed on, and your chocobo is in Free Stance, you will die).
On Free Stance, if you die, your chocobo will keep fighting the last thing you sent it at. If he kills that, he will just hang out with your body until you return, you get raised, or he times out(the later he disappears).
On Healer Stance, if you die, he will just sit there. Meaning, if he is on the hate list of any mobs (and since he was healing you, he is... He will just get railed into oblivion and take it like a champ. It is sad to watch, and I ussually Home Point immediately, as that will cause him to teleport out of combat right to me, and he will live.
On Healer Stance, while he still does the pee-pee dance when you get aggro, he will throw up regen, and if you do not engage the enemy, he may pull the mob off you onto him. So, when running through aggro areas, it can be funny, but just watch aggro when you are sitting around, your choco can get their butt kicked by mobs that you normally don't care about.
____________________________
http://na.finalfantasyxiv.com/lodestone/character/729735/