I used to have an Uzi carbine 'way back in the 80's. It has several major differences from the SMG which make most of the parts non-interchangable. As a carbine it is inferior to more traditional models of pistol caliber rifles, such as the M-1 carbine, the Camp Carbine and the 1894 carbine, due to a number of factors. These include weight, balance, and trigger pull.
Those of us Americans who want the SMG version can't go to Her Magesty's Royal Armoury and check one out like our friend British Soldier. For the SMG remember the $200 form 4 is not the big cost. Major expense will be the $6000+ to buy the gun itself. (This for a gun which costs The Queen about $500.)
So in that regard the carbine version has distinct advantages for an American who wants the Uzi look and doesn't mind shooting pie plate sized groups at 100 yards. Carbines can be had for less than 1000 dollars on a yellow form, but the SBR version is a little more plus the 200 dollar transfer tax for the form 4.
BTW, all Uzis are blow back action, but the carbines shoot on a closed bolt which is not interchangable with SMG open bolts.