It isn't just patterning differences, but the number of individual hits with individual wound channels. Given that both shots are on the money, the 12 will have two to three times that of the .410. That increases the likelihood of instantly decommissioning a BG.
You forget overpenetration. One reason for using shotgun pellets is to avoid shooting through a bg or walls and into whomever may be beyond.
No one is saying that a .410 is not a good option for those with unique physical demands.
If anyone wants to continue to trumpet the .4i0's superiority over the 12, please talk about what law enforcement agencies prefer.