It's interesting that you find the barre chord form of the F easier to play than the "open" F. It's usually the other way around. If you look at the open F, it's really just an abbreviated version of the barre F.

I think because you are doing a partial barre on the open F, it's easier and better to have your thumb on the back of the neck. I would say go with whatever feels most comfortable and allows you to get all of the strings to ring clearly.

Personally, I use whichever form requires the least amount of finger movement.