I use cautious officers on herons and drovers because I want them to stay away from anything that could kill them. Their fighters are more than enough value.
I have not noticed any behavioural differences between Steady-Cautious-Timid AIs when installed on a carrier set up the usual way (as in no offensive weapons that would compel the AI to move into weapon range of said weapons). Aggressive/Reckless will on the other hand drive the carrier into range where it can fire PD weapons offensively, wich is bad in almost all scenarios.
What I know for a fact tough is that if a carrier has any offensive weapon (I thinking about Swarmers/Annihalator cannon) and is not particularly good at close quarters combat (the only vanilla carrier that is actually good at that being the dreaded
Overridden Mora) , then cautious is the best option, as steady will get in closer than the ship's (lowest range offensive) weapon's range to the the enemy and timid will not engage it at all and will only ever use said weapons if the enemy is actively seeking to get in close.
Aggressive can surely work on dedicated combat carriers but I almost never pick that. A capital battlecarrier is basically a cruiser carrying a cruiser/destroyer sized carrier on its back and they're obviously not going to be the most suitable ship to be vulnerable to overextending due to their personality. And before you ask, no; Odissey to me is not a battlecarrier, it's a battlecruiser that gets a lot of quirks unique to it, including two fighter wings (therefore making it the strongest 40FP ship in vanilla IMO)
P.S: Timid/Cautious/Steady personalities just could vary in their "
social distancing" from the enemy if they're PD focused but I have not thoroughly tested that theory yet.