Nikon 300mm f4 AF-S vs Sigma 150-500 HSM OS APO?

Which one will better purchase?

We need additional information to better answer this question. What kind of camera do you have, and what would you be using this for exactly? Also do you need a 500mm lens or will a 300mm lens be good enough for what your doing?

With any of the above information I can tell you this:

The lower achievable aperture on the Nikon makes it fast than the Sigma's F/5.6-6.2.
That being said its also Sigma and personally I'm not a fan of there lens because of bad past experiences.

Without anymore information I would say to go for the Nikon lens.

The 300mm will be better optically because it doesn't zoom and will have better build and materials because its made by Nikon itself. The 150-500mm will pull objects closer to you at 500mm though but you wouldn't need that most of the time.