Huh?
To reload an AR-15, you have to drop a magazine, fetch the new one, get it into the magazine well and then find and release the bolt catch.
To reload a shotgun, you simply push rounds into the tube at any time the opportunity presents itself.
Four steps for the AR versus one step for the shotgun strongly suggests that the speed advantage will rest with the smaller number of discrete steps, so, yeah, it may well be quite deniable.
When you opened this thread, you said you wanted to hear from both "sides", yet no more than four posts later here you are advocating for one "side" against the other.
Are you really wanting a discussion?
Or are you looking the "evangelize" on behalf of the AR and argue with anyone who prefers a shotgun?
If it's an argument you're looking for, there is no shortage of people on this forum that will give it to you. But at the end of the day while the question can be discussed ad nauseum there can never be a definitive answer as to whether an AR or a shotgun is the "best" choice for use in an unspecified Home Defense situation because there are no parameters to determine what is "best" and that means all that will be accomplished is a lot of tail-chasing.
Enjoy your Sisyphean argument guys, as for me they just took some fresh-baked garlic rolls out of the oven, so I know where my attention is going to wander.