I shot the 120-300 for rugby and soccer (prior to owning a 400mm prime) on Canon. It is a nice lens for field sports, but of it suits you better than a 200-400 is hard to tell.
My shooting is more registration of the matches for my club and I tend to take photos all match long and try to get as many action shots of as many players. That also means I shoot when the players are on the other side of the pitch, for which 300mm is quite a bit less than 400 in practice, since I also need to crop and the less I need to crop, the better. (I shoot 45Mp R5). I you focus only on (relative) nearby action, the 120-300 would be my preference due to the 2.8 option over the 200-400.
You shoot multiple cameras, so it is also dependent on the lens you would use on the other camera. A 70-200 and 200-400 would give the best coverage. The 70-200 next to the 120-300 has far more overlap. The 200mm can cost you nearby shots, where most of the time you can get the best shots (scoring action, nearby so less atmospheric impact, filling the frame so less cropping). So I feel like you need a wider lens on the second cam next to the 200-400. A 24-70 or something is quite a gap to 200 and will result in heavy cropping probably. The 70 to 120 gap is better manageable.
If from my current gear I had to pick one camera and one lens to shoot a soccer or rugby match, I would pick the 120-300 on my R5. But I shoot with 2 cameras and have the 400 prime and a 70-200. On the 45 Mp R5 I can crop in on the 70-200 shots when needed and I prefer to handle the 70-200 next to the 400 as it is a lot smaller and lighter than the 120-300. But the 120-300 range appeals to me in addition to the 400 prime, but with rugby the 120 is a bit much when a try is scored right in front of me as well.
I'm not very familiar with the Nikon cams, but D5 or D850 can get away with f4 a lot of the time probably and if you really need 2.8 the 70-200 can still give you a set of usable images, just from a smaller portion of the pitch.
You have to determine what lens you would use next to either the 120-300 or the 200-400 and how important it is to you to cover a huge part of the pitch.
