In reply to GridNorth:
Well, yes and no. Petzl's recommended release method is identical to DMMs for the Pivot (not sure about BD, but I'll look it up).
The recommendation to use redirects and pulleys etc are all based on the premise that you can't unload it without mechanical assistance, in which case yes it becomes a complete faff. The biggest risk is when using the redirect/pulley method as most people recommend you use body weight to open the device, which then becomes very easy to lose control of, especially in a catastrophic case where the belayer is incapacitated or slips and fully weights the device effectively jamming it open, at the same time as they lose control of the rope. Hence they then get into the realms of prussic backups to prevent this. Someone posted a good video showing an alternative method a couple of months ago that used a different method than Petzl recommend that was a lot better. Note to self - I must look this up and have a play.
As a note, petzl's instructions don't detail using pulleys or redirects anywhere for the R4 - that's a hangover from the much earlier models.
IF you're releasing the device unassisted (as recommended by Petzl and DMM for their devices), anything happening that causes you to lose control would result in you letting go and the device locking. More or less exactly the same as the pivot, but the pivot's claimed advantage is that is requires less force/effort to open and so you should never be in the position where you can't open it and need to resort to mechanical assistance. Also that the ease of opening makes them more controllable.
re-instructors, I agree they generally know what they're doing - and I've used this method of releasing the reverso on rigging courses with no issues from the instructors.
How much better, if at all, the pivot is? No idea - like I say I'm waiting for a mate to fall foul of temptation and get one so that I can play with it.
Cheers!
Stuart