Both. Third person exclusively when traveling, or when in melee combat. Basically any time it's possible, because my character is not "me." This is someone whose "life story" I am privileged to share. And I find that certain actions, like jumping or walking across a narrow bridge, are much easier if one can see one's feet.

But, it's very difficult to do any kind of accurate ranged attack from the third person perspective, and camera motion tends to be a problem in close quarters like in dungeons. So, generally it's first person while sneaking around in dungeons, when using a bow or ranged magic, and when casting an unlocking spell on a container or door.
As Acadian says, the switching becomes almost second nature. I do it almost without thinking about it.
In my case, I came to The Elder Scrolls from prior RPGs. Most older RPGs are 2D 3rd person, often with parties of characters. Operating from a first person perspective in a 3D environment (as in Arena and Daggerfall) was a learning curve for me, and I was grateful that Morrowind and Oblivion gave me the option to go back to seeing my character. (I would not want to go back to 2D!

)