I had the same choice when I was looking for a lens for wildlife. I've not used the sigma so can't really comment on it, in the end I went for the nikon 300mm f4.
The nikon 300mm f4 is a great lens, its very sharp both with and without the 1.4 tc. i was previously using a nikon 70-300mm vr lens. I looked through my photos and found I used my zoom lens out at 300mm most the time, where its not at its best. The faster aperture is also useful for me as I usually try to be out for sunrise or sunset, the quality of the low light adds a little extra to the shot. Being able to drop the aperture down to get a faster shutter does come in handy at times. i use my 300mm for everything wildlife wise, its constantly attached to my camera. If I need extra focal length I attach the 1.4 TC. The 300mm f4 is probably one of the best nikon lenses for the money, it hasn't been updated with vr like the others but its still a great lens. Have a look on Flickr to see the images that people take with it, the quality is stunning and very inspiring too.
Whether a prime is right for you or not really depends on you, if you already have a zoom lens try using only one focal length to see how you get on. I do sometimes worry I may miss a shot once in a while by not being able to zoom out, but i find I think more about my positioning and composition now I only use a prime lens. I'm not going to say you can zoom with your legs like some say as its not always possible to do.
i feel the choice is down to which is best for you: a longer but slower zoom lens or shorter but faster prime lens that takes a TC well. which is best for you is down to your personal choice, the best lens will always the one you are going to take with you and use and not leave at home.
TBH you cant go far wrong with either lens, both seem to be equally good. Which ever lens you get, go out and enjoy using it.