Both.
I have AI behavior on my NPCs - mostly to make them wander around and doing various errants. I found it works well if they walk from house to house, opening and closing doors, and then simply wait inside for a random time.
I also use Behavior on my Player. My game has a point-to-click logic, so I have a tree on my player character that waits for events (see my other posting) related to clicking on the various hotspots, then sets NavMeshAgent targets on it (mostly using Seek) and further actions depending on the interaction - opening a door to enter somewhere, starting a conversation with an NPC, etc.
It may be easier to script it, but using Behavior Designer makes it easier to debug, and I like to re-use the same system, this way I can re-use Tasks between NPCs and the player.
Essentially, for many things I write Tasks instead of Monobehaviours and then hang them into the tree. I have a task that opens a door, walks through it, then closes it. I have a task that switches between an overhead and a close-up camera. I have a task that sets up the actors for a conversation, then starts that conversation, then tears down things afterwards, and so on.