Pro tip for turn in quests with Mouse/KB - Right click the empty slot for turn in and every copy of the item you have pops up in a convenient little drop-down menu.

Things you can't do nearly as easily with Controller.
-Micromanage placement of pets
-Heal alliance members (if there is a way, it's much more convoluted)
-Aim Caster LB.
-Aim things like cannons.
-Reaction times slowed on healer (Debatable if you have an amazing hotbar setup or great macros.)

Things you can do -
Sit on the couch.