My experience has been this:
When it comes to drops mobs do not drop crafting materials on you and chests do not hand out dyes or prisms when you run via trust, any chest that would otherwise give 2 pieces of loot only give 1 piece of loot which is actually not a problem because you are not competing for loot and it was going to take 11-12 runs to level out of a dungeon trust or not so you will still gear out regardless. Not to mention that the dungeon is a lot less likely to throw something at you that you already have. It does seem like the drop rate of weapons has been improved as my every trust run almost always ends with me getting 2 weapons from the dungeon.
As it is I am going to make a fair chunk of gil off of these trust runs, as I intend to later farm poetics to get ilvl 400 gear for my alt classes as the first 2 dungeons do not have gear that looks all that great anyways. Not to mention it gives me another centralized level "checkpoint".
The runs do take longer because of the lack of AoE, and that you cannot pull multiple groups. Not to mention of course the AI prioritizes dodging a mechanic before it will resume doing DPS. They do however make up for this by just hitting like trucks when they do DPS to make up for the time lost by doing mechanics.
When it comes to their AIs I do like that their personalities do shine through, however there is still things to gripe about. Urianger in particular needs to learn to identify what cards he draws. I keep seeing him throw melee cards on ranged characters and ranged cards on melee characters. Then again even when he gets it right you do not really feel the effect of the card and seeing him throw ewers on me keeps making me go "I do not even use MP Urianger... oh right..." Lyna and Alisae also are annoying in that the first chance they get on a boss they will fire off the LB unless you do it before they can start DPSing again while mechanics are ongoing.
Overall though the trust system is good and I hope they start expanding it over patches into the older content. While there is concern that doing so will hurt the socializing aspect of the game, it provides an alternative to things like palace of the dead and heaven on high for leveling DPS in a timely manner.