The question was a simple one, the OP has both guns, and wants to know the better choice between them. Therefore all answers about what to get don't help.
He said no kids, and will not be "house clearing", so both barrel length and concern about others in the house is irrelevant. He does, however have close neighbors, so penetration of walls is an issue.
"The shotgun is easier to hit with" is an old time honored statement. And even slightly true. However, in this case, its not important. With the smallest shot and the most open choke at across the room range, or at most, the length of the house, the pattern isn't going to be significantly larger than your open hand. If you are off target enough to miss with a single bullet, you are off target enough to miss with the bulk of the shot charge at inside the house range. And everyone here says bird shot isn't good for delf defense.
And, they are right, when you are talking about a couple of pellets. But with the mass of the shot still concentrated there is a considerable difference.
Momentum is a function of mass and velocity. Shotgun pellets are not a single mass weighing 1.25oz; but a collection of individual pellets weighing less than that (000 weighs about 71gr, #4 buck weighs about 19.5gr). So each individual pellet from a shotgun is going to be both lighter and slower than a 158gr bullet travelling at 1400fps. Shot will also be a lot less aerodynamic meaning that drag will rob them of velocity even more. As a result, a 158gr bullet at 1400fps is always going to have more momentum than any single pellet.
This is true, but again, at across the room range, it DOES NOT MATTER.
Given the situation described, waiting for the cops in your "safe" room, the shotgun is the best choice. Capacity doesn't matter much, as the odds of you shooting your gun dry are slim and none (and slim's out of town). Shortness isn't a big issue, as you are not going to be moving around in the house. Good sights are not an issue, as the range will be very short, and probably not well lit. Hunker down, and if they come through that last door, repel boarders. Your shotgun will do just fine, and due to the sheer mass of the projectiles will have as good (or better) an effect as any thing else you could use.
Slugs are not the best choice as there is about double the energy of the .44mag, and there is still enough left AFTER exiting your attacker to penetrate ordinary sheetrock walls and maybe ones next door as well.
I have one of those sweet little Marlin carbines, and its a great gun in a very good caliber for lots of things. And, if it was the only gun I had for home defense, it would serve quite well, and I would not feel un or underarmed at all. However since you do have a shotgun, I would choose it over the carbine, because of a few distinct advanges at very close range.