TTAG showed that any firearm with ammo designed for self defense is going to tear through interior walls. Some rounds will do it less than others, but they're all going to penetrate interior walls fairly easily. Ball ammo is going to penetrate the most, while hollow point and frangible rounds will break apart fastest, and hopefully stop before they go too far.
Maneuverability with a rifle will really depend on how the house is set up, and that's going to vary. I got taught to clear rooms with an M16A4, and while it's not the most comfortable, is doable. A 16" barreled AR-15 with a collapsed buttstock isn't difficult to use in most places, though still not as flexible as a pistol.
Noise and concussion are likely going to be bigger factors when considering a rifle for home defense. A centerfire firearm is going to suck indoors for your hearing, though you probably won't notice it immediately with adrenaline kicking in and auditory exclusion occurring. It's once the dust has settled that these things will come into play, since you're going to want to be able to hear where your wife and kids are, and be able to communicate. Pistol rounds are going to dull your hearing, while rifle rounds are probably going to leave you temporarily deaf. Fire enough rounds, and you're going to have very dulled hearing and a lot of tinnitus regardless of the caliber.
All that said, I'd rather lose some hearing than risk lose of life.
If you could use an SBR, then I pray you pay for a second tax stamp and put a suppressor on it. Shorter barrels have more concussion and flash, and while they're easier to use indoors, the after effects to you as the shooter are going to be worse as well. Even with a suppressed AR, the rounds are still going supersonic, and are going to cause some hearing loss and ringing in your ears. Still exponentially better than an unsuppressed AR, but don't think it's Hollywood quiet. Also, remember to take into consideration the added cost, length, and weight of a suppressor. Personally, I think it'd be worth it if I could afford it.
A few nice things about an AR for home defense is the added mag capacity, added lethality, and ability to mount a light and red dot. Makes shooting quickly and having fires dominance much easier. Downside is less maneuverability and increased noise/concussion.
Pistols can still have decent mag capacity, many models now have accessory rails, are very easy to maneuver with indoors, and have less noise/concussion. Downside is less ammo on hand, and pistol rounds are less effective (in general) than rifle rounds.
Figure out which is best for your situation based on how your home is set up, which you can use more easily and effectively, and what the most realistic scenario you'll have to deal with is. Then figure out an alternate plan if things get worse and you need to fall back on an alternate and tertiary plan.