The Pack offer +25% damage for melee/unarmed attacks and some damage resistance. They can also be the enforcement arm of the her government. I like their outfits and think they could operate very profitable adult oriented establishments in the Commonwealth which works for Nora's caps oriented outlook. However, I only use AP for walking around overencumbered so not really useful for me. The Disciples offer 25% AP restore for melee kills.
Operators are capitalists and will make the Commonwealth great again.
The Operator faction perk is great if you use suppressed weapons (+25% damage). The Pack have never had the opportunity to be appreciative in my games. Once you start making outposts, between the Disciples and Operators, the generic banter of the Operators is more appreciative of your work as Overboss.
You'll get two faction perks if you side with the NW Raiders and play their quests out.