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Nijisanji came first. Hololive came afterwards, and copied much of what Nijisanji did.
Over time, the two companies have become distinct.
Hololive is more like an idol agency. The girls are treated kind of like virtual idols. Hololive fans deny this, but that's the truth. Nijisanji talents are more like "streamers". Just like any streamer you'd find on twitch, or youtube or whatever.
While hololive strictly restricts intergender collabs, and has strict rules about openly talking about boyfriends and such, Nijisanji has no such rules. There are openly married Nijisanji talents for example. Guys and girls collab with each other all the time, in fact mixed-gender waves are commonplace.
While hololive has a ton of buildup before each generation releases, Nijisanji spams out waves of talents ever couple months with very little buildup. The disadvantage of this style is obvious, there's less hype for the debuts. But it also has advantages, as Nijisanji has over a hundred active talents. The NijiEN branch is 1/2 the age of the HoloEN branch, and they already have 2x as many talents.
In Hololive, the English branch is so weak, that fans are encouraged to watch the JP streamers during the excessive downtime. Whereas in Nijisanji, there is hardly any interaction or crossover between EN and JP whatsoever. The JP branch is so huge, even most JP talents wouldn't know another JP talent if you named them.
There also appears to be differences in compensation. Hololive talents are paid a salary, and thus have little incentive to actually stream beyond the minimum. Therefore in the English branch particularly, the girls only stream like 4 hours a week. While in Nijisanji, payment is based on performance, so the talents are heavily incentized to stream as many hours as possible. People like Pomu and Elira are putting in 35 hours a week.
Perhaps the most major difference is that in Nijisanji, the boys are much more popular than the girls. While in Hololive, the exact reverse is true.