In an ideal world where we could have full automatics for defensive use it would be great but not ideal.
I have never shot an Uzi, much less a full auto one.
But, one round of 3" 00 buck does about the equivalent of 9 or so rounds from the Uzi in one shot. Shot for shot you would have the Uzi outclassed for lead going down range.
You can choose between less lethal, birdshot, buck or slugs with a shotgun depending on how far you need to shoot, whether or not you need to kill, and what you are worried about shooting through.
Can't do that with the Uzi.