I know this has been using 5E rules, and while I currently GM 4E and I'm not trying to derail the discussion, I feel like I should add my 2¥. NOTE; I'm going to use 4E rules since that's what I'm familiar with, but I know the general principle of what I'm saying should still apply. If it's totally off the mark though, feel free to correct me or point out that it's not strictly relevant to 5E.
In general in my games regular street level Gangers and nooks would wear an armour vest or jacket at most, with only corporate or private security/police wearing heavier gear regularly. Likewise, they likely only carry light street weapons, handguns and shotguns and maybe the occasional smg. This will be relevant later.
Assuming a Runner is decent with a pistol, it has a Smartlink, and the enemy is moderately tough with an armour vest, you're probably looking at 8-12 dice to hit vs 3-5 to react and anywhere from 8-15 to soak the damage. So even with a Predator and it's -1 a and 5p damage base, they stand to soak a decent portion, or turn the damage to stun because of their armour rating. Again, 4E, convert to 5E as needed.
But here's the thing. A Runner using explosive rounds, which are pretty easy to acquire from a reliable arms dealer, or modifying the pistol for 3 round bursts, is going to increase that damage output decently. Hell, just carry a Predator with regular ammo abd the apprproate faje license, but if you can get them hide a clip of ADPS rounds in your shirt/jacket/crotch povket/etc. For special occasions. You've now turned your regular, everypne-has-one pistol into an armour-shredding hand cannon.
Likewise, if you know the enemy is wearing a bulletproof vest, pouring shot after shot into his torso is pretty damn ineffective, and the mark of an amateur. Treat armored thugs like zombies; aim for the head. Doesn't really matter how high-tech the armour is if they aren't wearing a helmet, and honestly, even modern day police with ballistic tac-vests don't wear helmets unless they're part of SWAT or specifically dealing with something that warrants a heavily armed response.
I'm not sure about 5E, but in 4E the rules to target an unarmoured portion were a -armour value do to the attacker. So a vest or jacket would be -6 or -8. But assuming the guy specializes in pistols, he could have an augmented 6 or 7 agility, 5 or 6 skill, Smartlink for +2, and he could even use the one simple action to aim abd then shoot. So with 13 to 15 dice, -8, you're still looking at 5 to 8 dice vs their reaction. Chances are you'll hit, and a shot to the face will make anyone have a bad day, even Trolly McBrickshithouse. Especially with specialized ammo.
Again, I'm aware 5E has limits to prevent the 4E exploding dice pool issue, but I'm sure similar situations and possibilities apply.
The long-winded point is this. Pistols aren't always as good for sheer damage as assault rifles or the like, but in the hands of someone who knows how to use them effectively, they can still be damn useful. And a Shadowrunner walking down the street with only a pistol will be much less noticed than carrying a big ass murdergun. And that clip of highly-illegal and highly-effective ADPS rounds for "special occasioms"? Easy to hide that pretty much anywhere.
There's a reason even modern military carry sidearms with multiple clips along with their main weapons. For long ranges or heavily armored targets, you'll have a hard time if it. But in short, carefully aimed and targeted shots, or in close ranges, or both, they can be extremely effective.
Again, if specifics of 5E rules and limits and such directly contradict or prevent what I'm trying to say, please point it out. But I think the theory still stands.