I've thought a lot about a situation like that myself. Especially something like a bank, or a restaurant. Someplace with lots of people, indifferent concealment, and very little I'd trust as cover. In the nightmare scenario, the robber shoots a bank teller or cashier or just somebody in their way, or a random person to make the point that "they're serious". At which point, it's anyone's guess whether he'll decide to keep shooting or not, and you kind of have to assume he will.
I think I'd have to align with the COM crowd on this. I'm moderately proficient, and usually calm under stress, but mental calm and physical calm are not the same; I anticipate being able to think, but I'm afraid my hands won't be as steady as normal. Since this is probable, I want to go for COM shots, and close the distance, and keep putting bullets into the target until the target is not a threat. Maybe that means he drops the gun and runs. Maybe that means a sucking chest wound and a muffled *thump* as he hits the ground. Don't care which.
Yeah, there are problems with the "close the distance" thing. I'm already a big target, and I'm just gonna get bigger as I get closer. That sucks, but it's a two-way street. Going with the assumption that he wasn't looking at me when I started moving, that should give me enough of an advantage to get several yards closer and get several shots in before he can react. If I am lucky, that will be enough. If I am not lucky, at least I still have the opportunity to get some rounds into him before I get tagged.
I guess the question for me is, "Walking Fire" or "Bum Rush"?
Walking fire, that is, moving forward at a walk while shooting (incidentally, I hear that sort of walking forward using the sides of your feet can give you better upper-body stability for fire) has the advantage of using my gun effectively for a longer time, getting more shots in. The disadvantage is that he can do the same if not quickly incapacitated.
Bum rush has a special attraction for me; I'm a big, heavy man and there are very few people on earth outside of Sumo rings that can remain standing after a diving tackle from me. The problem is that if I'm rushing him, I'm not shooting (because I know I can't control my fire at a run). So, should I fire several times first, then rush? I don't know. If my first shots don't put him down, that rush is going to leave me open to return fire.
I'm thinking it's probably a judgment call to be made at the moment. If it looks like he's likely to return fire before I can reach him with a rush, I would keep up the walking fire. If he looked rattled, but still upright, and unlikely to get his weapon in play before I could cross the remaining distance, I would try the rush for an immediate end to the threat.
That's my take, anyway.