Hmm... thought I had already commented in this thread many years ago.
In any case, as a Kansas City native: Arthur Bryant's for the meat, particularly a full slab to share and Gates for the sauce (either the hot or the regular sauce from Gates). The 16th & Brooklyn Bryant's location is relatively convenient en route to MCI, where I've been known to bring full slabs as my carry-on luggage for impromptu dinner parties after landing back East.
Gates will ship cases of sauce, which obviates the need to try to smuggle bottles past the liquid patrols at airport security. I've shipped Gates sauce as far as France before.