Farming for parts in BL2 vs. farming for anointments in BL3 are similar, but different, IMO.
The similarity between anointment vs. part farming, in my mind, is simply the farming part. That is, it’s a question of what you are farming.
Weapon parts and anointments are not functionally the same though, because whereas a Pimpernel is a Pimpernel is a Pimpernel (one set of parts and prefixes may perform slightly better than the other), a Wedding Invitation with a N2M anoint is much different than a Wedding Invitation with the 50% damage under 25% health anoint. In other words, anointments are much, much more varied and powerful than weapon parts, so with limited exceptions in BL3, it is not as much worth farming weapon parts and you farm the anointment you need for your build instead.
There were some scenarios in BL2 or TPS where if you didn’t have the correct parts, the weapon/item was not really worth using, or at the very least the weapon/item was much, much less effective without the correct prefix. Good examples:
Casual prefix on certain shotguns (Carnage, Swordsplosion, Butcher)
The Flying prefix on a Sand Hawk
Zero fuse time grenades
Weapon/item parts in BL2 were much less important overall than BL3’s anointments system IMO. If you are a min/maxer, then yes you will want those perfect parts in BL2, but it’s not like your build didn’t work without the correct weapon parts.
TLDR - Anointments literally can make or break a build in BL3, whereas in most cases in BL2 the specific weapon parts sought only made the weapon slightly better in terms of stats, but not completely unusable. This is the key difference I see between the two systems.