So let's look at the Renraku Red Samurai fighting each other. Body 5, Reaction 7, Willpower 4, Full Body Armor 10/8, and Nonconductivity 6 and shooting with 14 dice.
Shotgun with APDS, 7P -5AP. First shot 7 dice over, 2.33 net hits so 9.33P -5AP versus Soak 10. He takes 6P. Second shot does 10.33P versus Soak 10. He takes 7 damage. That's more than enough to take the target out. I will point out this is how much damage a SnS pistol does in a non-conductivity world (such if you're using book Red Samurai).
Shotgun with SnS, 6S -1/2AP. First shot is 8.33S -1/2AP versus Soak 15. He takes 3.33. He then makes a 19 dice and needs 3 hits. He'll make it. Second shot is 9.66S -1/2AP versus Soak 15. He takes 4.66. That's 7 damage total, not enough to take him out.
I will grant for stuff like shotguns, SnS is a very meh option in a Nonconductivity 6 world. You do have to live in such world and anyone who doesn't play in that world is boned.
Now let's make them Ares Cowboys armed with an actually good gun.
Ares Alpha with Shock Pad, Gas-Vent 3, Auto-adjusting Underbarrel Weight. That's 8 points of recoil compensation. Honestly, you could go lower on RC as long as you can hit 5 recoil RC. -3 dice to the second shot doesn't really matter at all. So you could do a AK-97 with Gas Vents 3, Underbarrel Weight, and stock if you wanted to save nuyen.
Alpha APDS 6P -5 AP. He'll start with a Long Narrow Burst (+5 DV) which does 11P -5AP base. After net hits, that's 13.33P damage versus Soak 10. That's 10 damage. The second shot is a Short Narrow Burst (+2 DV) which does 8P -5AP base. After net hits, that's 11.66P -5AP versus Soak 10. After 8.33 more damage the target is toast. Which is more than enough to kill the target.
Alpha SnS is 6P -1/2AP. He'll start with a Long Narrow Burst which does 11S -1/2AP. After net hits, that's 13.33P versus Soak 15. That's 8.33 damage. The second shot is a Shot Narrow Burst for 8S -1/2AP base. That's 12S -1/2AP versus Soak 15. Taking 7S for the KO.
The net result is pretty much the same. You take the target out after 1 pass. The only difference is 9Y (you'll have to fire 500 rounds for a squatter to lose a month of rent). Except, that's where a lot of beanies of SnS come into pay.
First off, the SnS works just as well in any firearm. Thus you can do Assault Rifle damage with a machine pistol, that's much more concealable. Secondly, it takes the target out alive. Even in a grimdark world, defeated foes you can kill later if you want is usually better than dead foes especially in a world of Mind Probe. If you run into a Force 6 spirit (which shouldn't be that uncommon), the APDS user needs 2 net hits to hurt the thing. The SnS user will hit if he connects and do more damage. A higher force spirit will rapidly be out of the reach of the APDS user while still a target for the SnS user. SnS is also restricted so you can use it with other restricted gear. How much you care varies (I tend to use illegal HV weaponary myself). The last thing is that the physical track goes longer than the willpower track as well. A 9 body 5 Willpower troll has a track of 13, but a Willpower roll of 11. That can make a big difference as well. All of this for an opportunity cost of 1Y a bullet.
Red Samurai like most unoptimized characters are huge glass cannons. Basically whoever goes first wins. If the target is actually tough enough to stand to AR fire, then SnS is going to be better. If the target full dodges, SnS is better since it cuts down on the defense check more and thus increases the chance of success on the follow up hit. Then again if they're active dodging, you've already won.
To wrap up my argument, in a game where people have poor gun choices, are glass cannons, aren't spirits, and wear nonconductivity 6, APDS is better. In a game where those aren't the case, SnS is better.