They would both work, and both are better than a short gun, but the edge goes to the .30-30 levergun for the simple reason that basically all .30-30 ammunition you buy is soft point or hollow point designed to expand well in medium size thin-skinned game. All of it has been tested and proven for that role going back a century. All of it will work exceptionally well for home defense.
In contrast, the majority of 7.62x39 is either straight FMJ or very crude HP/SP that may or may not reliably expand. It will be less effective and present greater overpenetration concerns.
The SKS obviously offers more capacity, esp if you add the mods for the 30 rounders. But you lose more ergonomics in the process and whether or not you would need that much firepower is another question. It's always a balancing act. Do you go with the lighter, handier platform with more reliable killing power in the first shots or do you go with a larger platform with more firepower. For most folk, probably the former.
although it never actually came to the shooting part.
It's that part that really counts, and personally I'd rather have a round I know will open up a chest and utterly destroy a circulatory system in one shot than an FMJ round that might or might not stop the attack.
If you do run with a x39, I would just say use the heavy corbon 150 sp's in x39 or some other high end hunt-proven SP. Don't follow the Hague Convention.
And of course the personal element is a HUGE factor. If you're used to leverguns, train with them and have killed many a critter with them, by all means use the levergun for your own defense. The last thing you want is to try to figure out a new system when it's really hitting the fan. And visa versa of course. Some would probably be surprised to see how well the old leverguns can work in a modern tacticool training course. Lower cap, yes, but fewer malfunctions and a very handy platform.