I can't comment specifically on either of these bivys but I've got the BD Lightsabre, which is a similar in design to the Bipod except that the Lightsabre has 2 poles. The additional pole extends forward from the hoop to raise the 'mini-tent' area a little bit more.
I really like the Lightsabre design. It keeps the material off the face and even allows enough movement for minor tasks (i.e. changing batteries in headlamp, peeling off layers, reading map/topo, etc.) while still comfortable in the bivy. The added weight of the small poles is fairly trivial.
Given my experience with the 2-pole bivy, I'd go with the Bipod over the Hooped Bivy.