Genuinely I see Bullet Club as a spiritual successor to the NWO. Aside from them co-opting black and white t-shirts and the hand gesture, they are the cool heels that turned into merch machines. Ironically, while without the NWO, a lot of factions that inspired even small bits of it later on (invading force i.e: Nexus, Rule-Breakers, DX, Cool heels, Undisputed Era) I argue Bullet Club has been overall more successful because of its longevity and overall better booking. It is almost thematic that Bullet Club has gone through multiple leaders (partially due to them being pursued by WWE and then the Elite splitting off to form AEW) but each era of Bullet Club has done a lot to help the faction evolve.
The original era with Prince Devitt at the top laid a lot of the groundwork. A group of mostly foreigners breaking all the conventions of New Japan.
Then AJ Styles came in and started to bring it further internationally and gave them their first taste of the IWGP Heavyweight Championship.
Kenny Omega, love him or hate him, alongside the Bucks they helped make them even more popular with their BTE series taking off and then Kenny had an arch. However, to a fault, their brand started to eclipse Bullet Club.
That is where the split came in (ironically, another comparison to the NWO) where it allowed the Elite to split off and do their own thing to continue their own momentum while...
Jay White appeared and brought Bullet Club back to its roots as a major antagonistic faction. Even there was an increase of Japanese talent in the group with KENTA, Gedo, EVIL, and SHO. While I think some of Bullet Club's booking has been fucked over recently due to the pandemic, and now they have 16 members, more than any other group in New Japan (probably due to half of them being stuck over-seas most of the time) they still remain an important part of New Japan and even internationally.
As for the NWO, there is no doubt they were important and great. They were the group that sparked wrestling's hottest boom period ever, but eventually, they fizzled out. They became too bloated. 29 different people within the first two years. That isn't even including some people who joined up with one group or another after their split. Then they were part of swerves upon swerves, a botched ending to the supposed climax of the story with Sting vs Hogan at Starrcade, and etc. In fact, Bullet Club has lasted longer than the NWO did.