Polygamy: Mormons, etc. generally opposes womens rights.
Polyamory: Ideally places noone above another, elevates everyone to have the healthy connections such that noone is a "3rd wheel" or more disposable. Less about "polycules" recruiting new members, and more about individuals pairing with new partners, and existing partners (initially at least) gaining a metaphor. Mileage may vary and the point is everyone's needs are a bit different and shouldnt feel pressured to fit neatly into a nuclear box.