This particular case is illustrative of a great range of problems with armed self defense.
Obviously, in an ideal world, we would be able to get the drop on the BG and wind up achieving three main goals: don't get shot first, make a solid hit on the BG, and don't get anyone else shot by you or the BG in the process. I think these goals may be extremely difficult, if not nearly impossible, to achieve in most cases.
The way I see it, the problem in this scenario is that the BGs are not expecting an armed response from anybody. If two men are robbing patrons in a restaurant table by table, then they are going to be very surprised by the sight of a gun or the sound of a gunshot. In an ideal scenario, then both BGs may be occupied with robbing patrons with their backs turned to you giving you opportunity to draw your weapon without attracting their attention, but as soon as you fire then a couple of things are likely to happen:
1. There is a chance you will miss, and wind up shooting someone other than a BG with your first shot
2. One (in the case that you didn't miss), or both (in case you missed) of the BGs are going to turn around and shoot back in your general direction. Since you are wary of collateral damage, you will be careful as to not to shoot in such a way that might endanger others, but the BGs are going to shoot rapidly and probably will hit other people that are at your table.
3. If you make a hit, there is always the chance that it overpenetrates and winds up hitting someone else.
4. Even if you make a hit, there are good chances the shot BG will remain able to shoot back.
Now in the process you may get off a second shot. Maybe you can get off the second shot and make a hit before the 2nd BG manages to shoot back, even if you make a hit on the first shot. Maybe you're Detective RIggs and you manage to get two BGs DRT with two shots that don't miss, ricochet, overpenetrate, or result in return fire.
IMHO, there are extremely high odds that someone other than the BG is going to get shot if you start shooting. If you get an unobstructed clear shot while the BGs are occupied looking in the other direction and you are a very good shot, you very well might make a solid hit with your first shot but unless you have an equally-positioned partner that is making a calculated shot at the other BG exactly when you shoot, then you can bank on return fire. And we all know what the odds are of a one shot stop.
In the end, I think if the BGs have not started shooting, then the chances that you manage to get out of this scenario having fired the first shot and not being blamed or held responsible for a number of other shots that may be fired are very, very low.
This is not like a crazed gunman scenario like Suzanna Hupp in Luby's. These are robbers using the threat of force, and it is unknown whether they have the will to actually shoot anyone. I am glad I don't have to make the choice about whether to shoot or not, and I certainly hope I never, ever find myself in this position, because I don't think there is any good answer. To shoot first will risk lives. To not shoot first also risks lives.
BTW, for those of you who think escape is the best option, I frankly think that trying to escape is just as likely to cause the BGs to start shooting as for you to start shooting yourself.