I'll try to get back on topic...God I hate stupid ninja rambos
I guess it's a range and threat ID issue. Close range and you know your threat you engage. Further range or it is unclear exactly where the shooter is you should move or take cover. Most CCW owners in a close up robbery situtation are better of engaging hoping they got the element of surprise on their side. Moving first would throw up a red flag to the BG, and your draw would be more noticed. I would engage first and move second.