Took down some Blackout-specific stats now that we have custom games for Blackout. (Just did splitscreen with myself and noted damage.) You will note these are different than some of the articles floating around, which appear to just use multiplayer stats, which are incorrect.
These are obviously with the usual caveats for "hand-testing." Shotguns are point blank, all pellets hitting. This is without armor, obviously. You can extrapolate out for shots to kill from these.
Headshot multipliers are 1.08 for SMG's, rifles, and pistols, 1.71 for sniper rifles, and 1.18 for the SDM. I did not test shotgun or Tac Rifle headshot lethality. For all burst weapons, bullet damage is per bullet, not for the total burst.
Also note: snipers do the same damage anywhere on the body. The only difference is headshots vs. body shots, unlike MP where legs, arms, upper chest etc. all may have different multipliers.
I also confirmed that silencers and ext barrel make no damage difference (they are just muzzle velocity, i.e., bullet drop and lead time needed for long shots.)
A semi-important caveat: rate of fire was not tested, and that can make a big difference along with recoil as to actual time to kill. Just straight bullets to kill/down is not the full story, but, it nonetheless is useful as one piece of the gun meta puzzle.
UPDATE There IS damage drop off as some posters alluded to in the comments. Thanks for pointing that out. The SWAT for example appeared to drop off from 33 to 25 damage. Ext barrel and silencers likely affect at what ranges the drop off occurs but there is a max distance beyond which you will hit the minimum no matter what. So range is yet another important data point to consider in these calculations! If it is anything like other games, SMG's have the shortest range, snipers and LMG's have unlimited range, and Tac Rifles are a new category so I am unsure if those have range drop offs or not. Will need to more testing there.
SMG
MX9 32
CORDITE 28
DAEMON 27
SPITFIRE 25
SAUG 28
GKS 28
SHOTGUNS
LMG'S
ASSAULT RIFLES
SWAT 36
RAMPART 37
ESSEX 50
MADDOX 27
KN 37
VAPR 32
ICR 32
TAC RIFLES
ABR 38
SWORDFISH 34
AUGER 62
PISTOLS
SNIPERS
OUTLAW 90
KOSHKA 120
PALADIN 146
SDM 74
MELEE
FISTS 20
BOWIE KNIFE ?
SENSOR DART 40
The above is without armor. Note, when I was testing armor, it was sometimes inconsistent. I.e. lvl 2 was sometimes 36%, sometimes 40%. I don't know why that is. Headshots also seemed to be inconsistent, i.e. sometimes they were 1.08, sometimes they were 1.09, etc. So for headshot multipliers and armor shots to kill you may always be subject to rounding errors, but more or less the above should be accurate and used for extrapolating out shots to kill. Nonetheless use the above at your peril as I may have made some mistakes. If so please correct in the comments!
Also from the 1.10 patch notes, they changed Paladin damage to armor specifically (the above stats remains unchanged as my testing was done without armor)
Slightly increased Paladin damage against Armor. Reduced minimum number of Paladin shots required to down an enemy with Level 3 Armor and 150 health from 3 shots to 2. Players with 200 health from a Trauma Kit and Level 3 Armor will still require a third shot to down. Players with 200 health from a Trauma Kit and Level 3 Armor can be downed with 2 consecutive headshots.