At the short ranges involved in home defense, I don't think any arguement against the .30Carbine round as "underpowered" is going to be an issue. However, nobody has just straight up said .30Carbine was underpowered in this thread... yet.
My Grandpa had a Carbine during the war and he always spoke highly of it. Grandpa was a truck driver... I found out recently he and his outfit operated out of Antwerp, Belgium between November 1944 and January 1945 and they had to fight there way to the outfits they were resupplying during the Battle of the Bulge.
2. Ammo is more lethal AP. SP, ballistic tip etc..
I don't know about you, but I'm not volunteering to get shot with any of it, 5.56 or .30Carbine. My Grandpa, whom I just told a little about, said they trained to kill a man at 400yds with the Carbine and he also didn't understand why Alabama didn't make .30Carbine legal to deer hunt. However, that may have more to do with the FMJ bullets whereas deer hunting generally requires an expanding bullet. To my understand though, all a projectile from BB size up to a semi-truck needs to be potentially lethal is 300fps.
4. More range 200 meters with longer barrels
This thread's topic puts the AR-15 and M-1 Carbine in the context of home defense. If you want to shoot an AR-15 to 200m, by all means do so, but to the best of my understanding, home defense distances are usually within 20'.
i voted m1 also cause i may feel the need to butt stroke somebody.
Not a bad idea. And this is just my observation, but some M1 Carbines have the bayonet lug too, but unless you've trained to fight that way... well, I think most home defense scenarios won't require it or offer time to fix bayonets and the DA's probably going to question motive and/or judgement on that one.
But let's remember, Kenshin did say "This is just a poll for fun."