Both burgers look great. I think I'd have to go with number 2 though. I've just never been a fan of barbecue sauce on a burger. But, with as many as it looks like you'll be making for this crew, I'm sure the sauce could easily be omitted on one of em.
They both look great. Not a fan of lamb except for chops and I prefer a burger I can actually fit in my mouth for a bite. Therefore, I would pick #1 but prefer a smashburger to both.