Here's a perspective from someone (me) whose favorite, like yours, is Giordano's, but who also likes Malnati's almost as much. I do consider them different styles, not interchangeable. When someone hasn't been to Chicago before, I generally prefer to expose them first to deep-dish from Malnati's (or the similar Pizano's or the original Uno or Due - all are related to the Malnati family, of course), just because that is more of the "classic" Chicago pizza to me. On a second visit, I'll take them to Giordano's.
However, you shouldn't take them to a place you don't like yourself. Period. It sounds like you have not been to Lou Malnati's, Pizano's, or Uno/Due. If that's correct, maybe it's time for you to try one of them, and this is a perfect opportunity.
Pequod's and Burt's are both single-crust "deep dish" style pizzas; I do not care for either of them much, because the "char" crust doesn't do it for me. Since you've already had Pequod's, you should be aware that Burt's is similar (again, not a surprise, since Burt started Pequod's many years ago). The biggest difference I noticed between Pequod's and Burt's is that Pequod's has a more concentrated tomato flavor in the sauce; the difference between the sauce on Pequod's and Burt's is like the difference between tomato sauce and canned tomatoes, if that makes sense.
I would NOT take them to Chicago Pizza and Oven Grinder (with their "pizza pot pie"), which to me is a gimmick of one place and not a fair representation of either style of Chicago pizza, deep dish or stuffed.
Gino's East... isn't bad, but I like Malnati's better. Oh, and I'm still not convinced they use any corn meal in their pizza. They sell their pizza frozen, and it has the characteristic yellow color, but the ingredients listed on the package do not include corn meal, only food coloring.
I haven't been to Art of Pizza, so I have no opinion about it either way.
So, if I were you, I would take them to the Malnati's near Blue Man, especially if you've never been to Malnati's. But if you don't like Malnati's, then take them to Giordano's. And if you want to take them on the "ultimate Chicago pizza experience", take them to both during their visit!
Remember, wherever you go, you can phone ahead with your pizza order. This avoids having to wait 30-45 minutes while seated for your pizza to bake. Incidentally, it also enables you to avoid any long lines waiting to be seated at Uno/Due in River North since they'll seat you in time for your pizza to come out of the oven.