Having used both, NACS is more compact, so both the port on the car and the end of the cable are significantly smaller than CCS. The cable itself is also lighter and more "usable" than CCS. At least at the newest V3 superchargers, the NACS cable is so much more flexible and easier to manage.
> the NACS cable is so much more flexible and easier to manage.
Nothing stops CCS from using smaller cables. Tesla tends to have cables which aren't rated for as long of lives with the plans on replacing them more often. Most CCS dispenser manufacturers chose beefier cables which were supposedly rated for longer lives, but environmental factors and people (ab)using the cables seems to lead to those cables not having anywhere near their rated lives.
I've seen some 50kW CCS chargers with downright flimsy cables, much smaller and thinner than most Tesla cables.
Tesla has thin cables at some superchargers. These are liquid cooled so they can get away with smaller wires. No idea if CCS1 chargers are using liquid cooling.
v4 are the new Superchargers, but they're mostly being installed in Europe where everything has been CCS for ages and Tesla needs the longer cable to support cars with ports in random corners.
Unless all these other manufacturers move their charging ports around in addition to switching connectors, the short cables on all the v3 Supercharger infrastructure is going to be an issue here for a while. If your port is in the wrong spot there's no way to reach without blocking two spaces.
Munro Live took both connectors apart and did an overview: https://www.youtube.com/watch?v=gmjofPpThWU