The first thing I would recommend is to get certified (you can find classes on the KCBS website) and then go judge. This isn't really a mystery, they are looking for good que, the same thing you are looking for.
When you bite into a piece of chicken is it juicy? I mean dribble down your chin juicy? Does the sauce overpower everything? Is there any particular spice that stands out from your rubs or seasonings? Is it too hot?
Tenderness is the easy part IMHO. The rib shouldn't fall off the bone, but should leave a perfect bite mark and the bone should dry quickly after the first bite. Brisket uses the pull test, does it pull apart or is it a rubber band or does it fall apart when you pick it up? Chicken the big idea is skin, can you bite through it without getting a chin flap? The big mystery on chicken is crispy skin which just simply doesn't come from a smoker, but you should still be able to bit through it. Pulled pork should not be chewy, but it should not by mushy. If you've had mushy pork, you'd know it. It will also leave your mouth feeling dry after you eat it.
There's my .02...
Nothing I like more than to kick back with a Zima and a Virgina Slim reading 50 Shades of Grey with DCman (The Czar).
And on the eighth day God created barbecue …. because he DOES love us and he wants us to be happy.
Current smokers: Egor (trailered RF) and Easybake (tabletop pellet drive)