This is what I know.
[b]Hidden Hand[/b] increases aim assist or a part of it. Depending on what it affects, it [i]may [/i]increase bullet pull, which is a part of aim assist. Snipers [i]almost [/i]completely lack bullet pull, but I'm not sure about other special weapons (but considering the gameplay style and usage of shotguns and FR's, it's probably not too important).
The [b]range stat[/b] does [i]not [/i]increase your aim assist, but instead maintains it. If your weapon has low range than you lose aim assist when aiming at far off targets. In this sense you could say the range stat [i]theoretically [/i]governs hitbox size at a distance, but mechanically speaking it works a bit different under the hood. Actual character hitbox sizes NEVER change. Programming such a thing efficiently would be a nightmare, and it's not needed.
When you [b]zoom [/b], many things like recoil, sensitivity, accuracy, etc are scaled to provide a consistent experience. Zoom has the effect of "pretending you're closer." This means the ONLY time zoom is not beneficial is when your target is so close that the reduced field of view disorients you or you can't aim quick enough. Therefore, simply changing to a ranged scope can let you use Doctrine on a map like Widow's Court!
[b]Rangefinder [/b]is a perk that increases zoom. It's probably necessary for an enjoyable hand cannon experience (because the zoom has been nerfed in the past). Unfortunately it only adds 0.1x or 10% more zoom (not sure), which makes it a weak perk on other primaries that have scopes anyway (IMO).
There are some exceptions like Vex Mythoclast, but most all primaries, snipers, shotguns, Hakke sidearms, and machine guns are [b]hitscan[/b]. When you fire a shot (out of your face), the game usually calculates a simple vector in the 3D space. If this 3D line intersects your opponent's hitbox, the shot (should) register. [u]The length of this line (usually in meters) is divided by your zoom to provide a new engagement distance, then this distance is applied to your weapon's "range curve" (based on its weapon class and range stat) for things like damage falloff, aim assist falloff (which affects bullet pull), etc.[/u]
"Pretending to be closer" is [i]currently [/i][b]MUCH [/b]more effective than increasing your range stat. This applies to all scopes and weapons, including shotguns!
Shotgun engagement distance:
Hipfire: 1x
ADS: 0.83x
Rangefinder: 0.77x
Universal Remote: 0.71x
Above: This is how [b]Universal Remote[/b] deals superior damage from afar. You MUST be ADS to take advantage or suffer from the below-average range stat. UR has 0 aim assist to allow quick aiming even with the increased zoom. You should only hipfire UR against critically weak enemies, or if you're very close and intend to follow up with a melee. The range perks are still crucial for UR's performance (probably). Due to pellet spread, its 1-shot kill range is actually really similar to the other shotguns but it's 2-shot kill range is noticeably farther.
Let's suppose you can get a 1-shot kill at 1.5 meters. How is this affected by your zoom modified engagement distance? It's actually just kill range*zoom.
Hipfire: 1.5m
ADS: 1.8m
Rangefinder: 1.95x
Universal Remote: 2.1x
We can see here that ALL [b]shotguns[/b] become MUCH better when aimed, and UR is good for fighting other shotguns that lack max range (32) and Rangefinder.
Did you know? Despite its small impact bar, the Universal Remote actually deals as much damage as Found Verdict! It's impact bar may be misleading on purpose, to match with the description. It looks like a junker, but it's really a beast!
[b]Invective[/b]'s normal shots are ~14% weaker than Felwinter's Lie, but the final round is ~15% stronger! The final round is much easier to abuse because of the ammo regeneration and small magazine. Abuse it often! I like to reload 2 shells at a time, because just 1 is plain risky.
[b]Lord of Wolves[/b] is not really a shotgun! Its statistics are therefore misleading. It actually fires clamped fusion bolts, meaning your maximum range NEVER changes, and your bolts will ALWAYS be the slowest in the game. The useless range stat and burst fire BEG for you to choose smart drift control and perfect balance to take control. The impact stat is high for a shotgun (*12 pellets), but actually unimpressive for an FR (*7 bolts). FR's require 4/7 (raid FR), 5/7 (most FR's), or 6/7 (Split Shifter Pro) bolts to kill. But what's this? LoW requires 5/5 bolts to kill, which is very difficult due to the bolt travel time. Add in the fact that you're actually aiming this weapon (it's not spread fire) in close quarters engagements (which requires better dexterity than using a sniper) and it's no surprise that most LoW kills for most players end up taking 2 bursts, which is barely faster than a primary, and slower than TLW! And that's why LoW is not meta. All of LoW's effective ranges are covered better by other weapons: shotguns, sidearms, TLW, FR's. Lastly, you can 2-burst supers with this weapon.
[u]DLC:[/u]
[b]Red Spectre[/b] really is a prototype, with 1.7x base zoom (like a PR instead of an AR). Is the +.2x zoom worth it?... Nah.
[b]Accuracy[/b] is how close your bullets go to the reticle when you fire. Things like bullet pull are applied later. Having high aim assist can [i]slightly [/i]counter bad accuracy (of a primary weapon or player), but to land ALL your shots you'll need both. I find that accuracy is more important. You can improve your aim, but you can't improve bullet pull!
[b]Doctrine of Passing[/b] is the only meta AR that can have both Persistence and Counterbalance, making it superior at landing mid-long range shots. I find the recoil direction (with Counterbalance) also conveniently matches the swivel direction of my thumb for easy control.
[b]Arminius-D[/b] has higher equip speed, aim assist, magazine, and can roll with crowd control, making it a multi-kill monster. But it's ugly, and the scopes/higher muzzle flash are disorienting (kind of like NLB, though less obnoxious). If you can aim an Arminius-D with High Caliber Rounds (instead of Braced Frame), you will be [i]unstoppable [/i](good luck with that).
[b]Hand cannons[/b] lose accuracy when fired quickly, and lose kill power when fired slowly... so they suck IMO. [b]The Last Word[/b] is different because of its Fan Fire perk. It shoots so fast that it kills faster and lacks the normal miss penalty, making it meta. I find the Doctrine more reliable and easy to use, though.
[b]Inventory [/b]is a hidden stat that generally determines how much ammo you spawn with and how much you can get at a crate. It's a fairly useless stat on primaries but having more special ammo can REALLY help in both PvE and PvP. You can view base/minimum/maximum inventory stats of weapons [url=http://db.destinytracker.com/]here[/url]. The data below has been gathered from the internets and may be incomplete/inaccurate.
[u]Perks[/u]
Send It: [b]-15[/b] inventory
Skip Rounds: [b]+5[/b] inventory
(Specific Special) Ammo: [b]+20[/b] inventory
Special Ammo: [b]+30[/b] inventory (only available on certain year 1 and exotic armor)
Field Scout: [b]+50[/b] inventory (Working as intended! Not useless!)
[u]Snipers[/u]
Ammo on initial spawn:
Default: [b]6 [/b]rounds
95+ inventory: [b]9 [/b]rounds
100+ inventory: [b]12[/b] rounds
Ammo per crate:
Default: [b]3 [/b]rounds
Longbow Synthesis: 3 rounds
30+ inventory: [b]4[/b] rounds
100+ inventory: [b]5[/b] rounds (unconfirmed)
[u]Shotguns[/u]
Ammo on initial spawn:
Default: [b]7 [/b]rounds
UR: 12 rounds
99+ inventory: [b]13 [/b]rounds
100+ inventory: [b]14 [/b]rounds
Ammo per crate:
Default: [b]4 [/b]rounds
80+ inventory: [b]5[/b] rounds
90+ inventory: [b]6[/b] rounds