I am 100% in on Bieniemy.
I'm a big Andy Reid fan, always have been. If Bieniemy brings nothing else to the table, he would still be installing a system that has been at least marginally successful with just about every quarterback its ever featured. I'm talking Kevin-Kolb-is-an-NFL-quarterback successful. I can't believe that Bieniemy hasn't absorbed at least a little bit of Reid's approach to developing quarterbacks.
Also, Reid is almost universally respected within the NFL. That's absurdly rare. That's why I think Reid's coaching tree has been more successful than someone like Belichick's. Every single coach off of Belichick's tree has inherited his absolute cuntiness and tried to replicate that culture - none have been successful on the NFL level. Reid has John Harbaugh, who is respected by his team and has won a ring. Reid has Doug Pederson, who is respected by his team and has won a ring. Reid has Sean McDermott who, whatever you have to say about him this early in his career, clearly has put his young quarterback in the best possible position to be successful. I don't know why you wouldn't want to take a chance on a branch from that tree, especially when you're talking about Reid's most overwhelmingly successful assistant to date.