I don't see the use for pistol caliber carbines given all the compact 223s that are around. There was a push for the former when it was thought by some agencies that 223s were too militarisitic in public opinion and/or their government (city, state) went along with that.
But the inability to deal with body armor as in North Hollywood argued against the pistol round. I recall that when the Ruger 9s and 40 long arms were being pushed, I read a review that acknowledged the problem but said well - with the better accuracy, you could the guy in the leg. Oh, well.
So, the classic debate is 223 vs. 12 gauge. The argument from the latter is usually its awesome stopping power, the scary sound of the rack and you don't have to aim it.
However, users know it's not that easy and the shotgun takes some skill also.
Either gun works if you know how to use it for most HD. Probably the North Hollywood guys aren't coming to your house. Just avoid the 12 gauge argument as the hammer of Thor for the unskilled.