func_static will make complex objects more easily selectable and you can set them to not have collisions, which can be good for multiplayer and singleplayer, particularly for details that are too small to interact with or will be covered with clip brushes
detail will make the brush not be included in the BSP compilation and will reduce the complexity of the portaling process
something to note is that func_static will be rendered on both sides of a visportal if it spans the visportal, for instance a door frame, if made a func_static, will be rendered on both sides of the portal, but this applies to any object, so a big rooftop will also render on both sides. I hope that makes sense.
finally, func_static are entities, so they will increase your entity count, which may be relevant in situations where you are saving the game etc. since doom 3 has an entity count limit of 1024 or something like that. so lights, models, monster all count toward this total (basically anything you see when you press "i" in the radiant)
Generally speaking, stick to the detail method as much as possible, and use func_static when you need more control over how the geometry is being rendered or interacted with