Lately I'm thinking they won't try to compete too directly for now. Cover gave NijiEN auditions a couple months before they opened their own auditions for HoloEN Gen2, so they'd really need to rush to get the new gen ready as soon as NijiEN launches. It'd be cool to see both companies compete hard for viewers, but intercompany collabs are one of the biggest spectacles they could do and the EN market is a little short on that end. Currently, VShojo is mostly based on Twitch and everyone else is around Asian time zones.
See, I've been thinking about this ever since reading a post on facebook. People dismissed Yagoo's idol group ambition so easily since people thought idol group must be all seiso, but AKB in its early days was pretty wild, with something like Haachama cooking or eating weird stuff were not that rare. Hell, they even made a dorama about their idol playing student delinquent beating each other fist to fist.
Meanwhile, Niji is more like generic japanese talent agency. If you've watched Downtown or Gaki no Tsukai, you most likely knew about company such as Yoshimoto. Niji with its huge roster is reminiscent with that kind of company.
Now then, however, after the shitfest that was CN, holo/cover finally wisened up. They realized that each branch can't just walk alone, they need synergy to become unique. That's why after CN, JP branches frequently collabed with ID, creating storylines and moments that pushed ID to broader audience. In fact, the success of ID2 happened because of the synergy between JP-ID-EN collabs.
On the contrary, due to its huge roster and a culture that possibly similar to a normal talent agency, Niji didn't have that same kind of synergy. Japanese talent agency tends to be very cliquey with big names having their own followers and junior "underling", and the same might be possible happening in Niji. That's why you can't see any synergy or big names helping lower branch/talent to bigger audience (just look at NijiID's growth and HoloID)
Now then, what would it meant with their new EN groups? We can see the same playbook of ID2 as with EN2, with everyone from Holo including Stars helping promoting it. Niji, due to its focus on domestic audience and lesser EOPs presence, might be falling behind in this regard. But they're hiring official clippers (no matter how idiotic it was), so I'm thinking they're going to copy Holo's playbook. A genius move from Ichikara, however, if they decided to team up or did some networking with traditional streamers, but that would open a whole new can of worms
