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Save up for the 50-500 OS. It's a great one. If you can't afford to save up for that, compromise and get the Nikon 300mm f/4, a used one can be a great buy, and it's very sharp--it just lacks stabilization.
Imho the 120-400 is probably better than the 150-500, but I don't like either. Both produce pics which, like you said, are very flat and not too contrasty. And really need to be at f/8 on the long end to be decent. And even then, are only just decent.
They really lack that "special sauce" that the new Sigma glass has. I had a 150-500mm OS that I used on a Canon camera, back in the day. I kept it for like...oh...a week. Before I returned it. To put it mildly, it sucked. Badly. Sigma really dropped the ball with those lenses imho. I don't know what the deal w/them is, but they need re-done.
Again, if your budget is less than 1k, look for a used nikkor 300mm f/4... If you want stabilization and can save up a little, get a 50-500 OS. Or wait for one to appear on the Sigma refurb page. The 50-500 OS will rock your world. It's so much better. Not even in the same league as the 150-500. Granted, you won't get sharp corners at 500mm. But, who cares. It's sooo much better than you'd think it could ever be. Biggest downside is f/6.3 comes at like...225mm. But then again, you get an extremely good macro mode, so whatever. D800 sample from 50-500 OS, it's about a 50% crop, this guy was about 1/2 the way down the frame toward the bottom left corner, at 500mm f/8 I believe. (I now use a 120-300 2.8, but sometimes I miss the convenience of the 50-500).