Carbine
Disclaimer: I don't own a shotgun yet.
I've had to evaluate HD in three different dwellings since I started shooting with any regularity.
In the first place, I had an easy 60-foot unobstructed shot from my bedroom door to the front door, and the home layout included no stairs. Exterior walls were all brick. And if you had to "take it outside," the whole neighborhood was brick, and laid out in a rifle-friendly fashion, and there were many mature (large) trees. It was just about as ideal a carbine environment as I've seen.
I had my pick of carbines, ranging from a couple in 9mm to a lever gun in .30-30, with a 5.56 and .357 in between. The one with which I found myself most comfortable was the M1 Carbine, even though I also had a CX-4 available. The M1 Carbine fit me naturally, was easy to "sight and sling," while the CX-4 was oddly kinda ergonomically awkward.
Since then, having had more opportunity to shoot the CX-4, I believe that with a bit of training and practice, it would do nicely. It is, after all, a nice piece. It may be "ergonomic" but that doesn't imply "natural" in handling.
We moved a few years later, and I found myself assessing HD in a tri-level, where
everything was cramped. Not good for a long gun at all, really. So the S&W 586 became the go-to HD thing, and the M1 Carbine took second. The neighborhood was distinctly different, and any outdoor work was going to require real care and accuracy, as the homes were all made of tissue paper, and organized so as to present Murphy's Maximum Risk.
We are now living in a place with a main floor and a finished basement, but with a whole lot of open space again. Neighborhood is a mix of brick and tissue paper (mostly paper), but the layout isn't too bad. Still, you'd wanna be
very "rule four" about any shots taken outdoors.
In this environment, I once again lean toward the carbine. There's a 45-or-50-foot shot from the master bedroom to the front door. However, there are stairs. It is conceivable that someone who knew what he was looking for might believe he could get downstairs, back upstairs, and out the front door undetected. If that proved to be false (wife is light sleeper), I wouldn't head downstairs with a carbine (even though the basement is mostly open space). The Smith gets the nod for that.
Consequently, what stays closest mostest is the .357, while the carbine stays handy.
If for any reason I believed that any part of the action would take place outside, I'd grab the carbine.
The scenario would first have to have Hollywood approval, as I don't know what kind of event would get me to run outside in bathrobe + skivvies (even in a town as small as ours) chasin' after bad guys.