I don't think I've ever seen the floppies, LOL.
I've don't particularly like the neck strap with line/rein rings at all. I've always felt that they "broke the line" between the bit and the saddle terrets and the hand even more than normal. But maybe I've had them set wrong? I don't know. I've seen a good line between the horse's bit and the saddle terrets back to the hands and I've seen "broken" lines. Think it really depends on what you are doing with your driving as to much you see this and whether it works for you. Also, the "broken line" seems more common with the little guys than with the biggies - think it's due to the length and set/carriage of the little's necks.