To my ears, whether something "swings" or not is not part of my sense of East Coast VS West Coast. In general, East Coast is simply more blues based and has a harder beat. When I was young and first getting into jazz at the end of the '50s and early '60s (yes frogman, I've got several years on you), the debate over the merits of each style was well underway. For me, Brubeck, Mulligan/Baker, and others could certainly swing. Maybe it was more the absence of that hard beat that contributed to the "cool" label?
Now I've lived on both coasts. When you get within a mile or two of the Atlantic you can smell it (the sea air I mean, not backwater bilge). However here by the Pacific I can be within a city block and not be so aware of it. I don't know if the Atlantic is briner but in general the East Coast has higher humidity and I suspect that greater moisture in the air carries the salt smells.
I bring that up because it suggests other characteristics to me. NYC is known to be loud, up front, in your face, while LA has the reputation to be laid back, relaxed, and yes, cool. Whether those are fair characterizations or not, they have also been applied to the jazz associated with each. The simplest difference may be that East Coast jazz tends to be more intense.
With all that, should I guess that Bruce Katz is from California?