I have tried both and I like the Nurtural No-Bit bridle
better. The bridle is overall more adjustable and the grippy stuff under the nose helps keep everything in place better. I also like that the cross under pieces can be shortened. On my Cook biothane they can't, and my reins end up swinging from the weight of the ring and my rein snaps.
My horse seems to respond the same to both bridles. She does stop a bit better with the nurtural when she's excited, lol. I think it's because of the grippy noseband, keeping things in place so she can feel the pull better.
I have the biothane of both. I don't like the reins with either one thought. I like my leather reins, just personal preference