Having to control both character's dialogue choices was one of my main complaints when I first started playing. The patch made it better but I still don't know how much of a difference the different personality types made. I picked free for my second player but after having to redo an section over I noticed that his dialogue choices changed. I checked by reloading again and once again his choices were random. I expected them to be fixed choices but to do that the devs would have to go through each line of dialogue and assign it to specific personality. That would take a ton of time and I imagine if they ever get to it it's low on the totem pole. Until then, it seems the 2nd player's dialogue choices are random.
This might help though choosing AI personalities.
However loyal as mentioned above will ensure they always agree with your decisions. IMHO however that defeats the purpose of having AI profiles in the first place and takes away from the RPG nature of having a party.