One obvious characteristic that occurred to me shortly after posting my previous reply is crust thickness. Thinner generally means crispier. It's possible to make thick-crust pizzas that have an element of crispness, but I'd say it's almost impossible to make a thick-crust pizza that doesn't also have bready qualities, either exclusively or in addition to the crispness.
I thought about adding this characteristic to my list last night, but I had to sleep on it first: Lamination. Not all laminated crusts are the same, so some of what I'm about to say may be untrue in certain contexts. But mostly I won't steer you wrong.
There are three members on these boards who I'd say stand out pretty clearly as the most experienced, most passionate, most knowledgeable makers of laminated pizza: 1) fazzari, who owns a pizzeria that produces very low-hydration laminated pizzas, which seem to be similar to Shakey's pizza, but probably much better; 2) DNA Dan, who specializes in a softer laminated crust, much more like Round Table than Shakey's; and 3) Aimless Ryan (me), who has spent the last three years obsessively trying to figure out how to clone Tommy's Pizza (Columbus, Ohio), which I suppose could be called a hybrid of Shakey's and Round Table. There may be some other laminated cracker style freaks out there, but no one else immediately comes to mind. Although Peter (Pete-zza) does not really specialize in laminated cracker style, you can pretty much trust anything Peter has to say about either this style or any other style of pizza. Oh yeah, and elsegundo. He's not very active on the boards, but elsegundo has contributed a ton of unbelievably useful information about Shakey's and Round Table, along with proof (pictures) that support his claims.
Since fazzari owns a very successful pizzeria, he obviously has infinitely more experience than either me or Dan. Fazzari (John) obviously knows his stuff, and his contributions are amazing, but I think sometimes he gets a little tunnel vision and forgets that his favorite pizza characteristics are not necessarily the same characteristics other people may seek. However, in his defense, the Yelp reviews for his pizzeria average more than 4.5 stars. I don't think I've ever seen any other business that averages more than 4.5 stars on Yelp (except maybe In-N-Out), so that should tell you something I can't put into words. Read his posts.
DNA Dan does not own a pizzeria, but he does own a sheeter and a conveyor oven. Even though Dan produces almost infinitely fewer pizzas than fazzari, Dan is clearly very passionate about his malty, laminated, beer crust pizzas. His malty laminated beer thread is a great thread, and he has also contributed a lot of great content to other cracker style threads (mainly Shakey's and Round Table threads).
I know some stuff too. I don't have access to either a commercial oven or a sheeter, but I feel pretty confident that my cracker style contributions should be very useful to someone like yourself. If you look through the Tommy's thread, you'll quickly see that I don't withhold anything. I'm very thorough, I use a lot of words, and I share a lot of pictures. My best work by far has occurred over the last two or three months, so you might want to start out by looking through the last couple pages of the Tommy's thread (July-September 2013), before starting over at the beginning of the thread to see the evolution of how I got to the point where I can honestly say my Tommy's style pizzas are about 95% identical to actual Tommy's pizzas (and probably a lot better than Tommy's).
With the kind of laminated crust I do (or used to do), the crust tends to end up with several distinct dimensions of crispness. The bottom layer is very crisp, but the layers above it are progressively softer and chewier. It's a nice effect that you almost can't get anywhere anymore. My more recent laminated pizzas lean toward crispy/flaky all the way through (and are much thinner than earlier versions). I assume Dan's version of laminated pizza has the crispy-to-soft texture or effect (because his pizzas are thicker and softer than mine), and I assume fazzari's version does not have a crispy-to-soft effect (because he uses such a low-hydration dough).
Anyway, if there's one thing I wanted you to take from this long post, it's LAMINATION. Not enough people know the joy of laminated pizza crust. You owe it to yourself, your family, and your friends. Trust in lamination.