I would say the E1e clip is the more secure of the two. It has more pressure and the body has knurling.
With that being said, I love the E1B clip and hate the E1e's. But I greatly prefer bezel-down carry.
If security is your #1 priority, the E1e's is more secure.
-Robert
EDIT: Okay, I just did a little test. I tried clipping both my E1B and E1e to some PJ pants pockets and then held them upside down. Here are the results:
E1e (bezel-up): Held on to the pants the absolute best, even with some shaking.
E1B (bezel-up): It held surprising well, not not as well as the E1e.
E1B (bezel-down): It didn't hold at all. Once the pants were upside, it slides right off the pocket.