Depends on the camera and the circumstances...
If I'm shooting my Leica III, I nearly always have my Nikon Varifocal finder on it, and am using that to frame the shot... given that additional displacement of the camera body to the side (when held vertically), and my big schnozz, I probably wind-up shooting over-arm most of the time, so that my nose doesn't keep the camera body too far from my face/eye.
I'm right-eyed too, which also plays-in to that...
If I were left-eyed, I would probably tend to shoot under-arm, again, keeping the camera body away from my big nose...
( Come to think of it, this would go for all my eye-level finder cameras...)
I usually focus in the horizontal (relying mostly on vertical lines in the shot for RF sighting), then frame and shoot vertical... I'm not fast.
If the shot has more horizontal lines than vertical, I might focus holding camera vertical, even if I will take the shot in horizontal... depends on what makes focus easiest. Again, I'm not fast about it...
These days, if I'm shooting the Leica, I'm going for "art" or historical record, so I will take more time with the shot; I've consigned most of my casual snapshots to my "antique" digi-cam: a Canon G-1 Powershot.
Regards,
Luddite Frank