False grip on bars

What is a more proper false grip on a straight bar: thumb wrapped around the bar, or thumb over the bar with the other fingers? I’m guessing thumb around the bar, as it gives you a more secure grip?

While straight arm hanging under the bar in a false grip with the thumb around the bar, I feel a lot of strain on the thumb, and where it connects to the wrist. I’m wondering if there is a warmup that targets that specific point of the wrist and thumb? Thank you!  

It depends on the thickness of the bar and on the wrist mobility. if you can show a false grip plus a good radial deviation then variation with thumbs down it is more effective.