Just for fun, although it would be cool if the factions had some unique perks for their weapons and equipment.

For example:

Omolon
Bungie's theme: Mad science! Integrate with guardians abilities
Perk: Arc Amp
Kills with arc abilities change weapon damage type to arc for 10 seconds

New Monarchy
Bungie's theme: None right now, but NM seems to emphasize leadership and teamwork
Perk: Lead from the front
Allies in close proximity take less damage when they are behind the wearer.

Dead Orbit
Bungie's Theme: None right now, but DO seems to emphasize mobility and exploration
Perk: Stare into the Abyss
While Sprinting, gain advanced tracking

FWC
Bungie's Theme: None right now, but FWC seems to emphasize combat and temporal schennanigans
Perk: Schrodinger's bullet
Rounds have a small chance of splitting into 3, each on a slightly different trajectory. Only the bullet that does the most damage will have that damage applied.

I can't think of any right off the top of my head, so I'll have to ponder, but I like the ones you've come up with.

This is the sort of stuff I hope we see in Destiny 2. Make me actually care about and feel involved in the factions I choose.

Factions:

• New Monarchy
  Armor Perk: The Regiment
  Do increased damage against enemies already damaged by allies. Gain more Super energy from Assists.
  
  
• Dead Orbit
  Armor Perk: No Turning Back
  Greatly increased armor when player is the last living member of their Fireteam. Grants the user +2 Agility.
  
  
• Future War Cult
  Armor Perk: To War
  All ammo pickups have a chance to grant extra ammo. +1 Recovery.

*Armor perks do not stack. Only one faction perk can be active at any time (determined by currently-allied faction).

Foundries:

• Häkke:
  Weapon Perk: More Däkka
  Missed rounds have a slight chance to be returned to the magazine. (Mulligan as an intrinsic perk across all weapons, even Auto Rifles. Can stack with actual Mulligan perk).
  
  
• Suros:
  Weapon Perk: And Look Good Doing It.
  Doing damage with Suros weapons has a chance to return a slight amount of health, but does not trigger health regeneration (Reduced Recovery stat while weapon is equipped).
  
  
• Omolon:
  Weapon Perk: Shmafety First
  Rapidly firing the weapon without manual reloading causes it to overheat, dealing increased damage, but with a chance to damage the user.