All of the Nikkor 500mm f/4 lenses even going back to the P (manual focus) or AF-I series are fantastic optically and take teleconverters just fine (at least the TC-14 and maybe the TC-17 but that's personal taste) But when you go farther back than the AF-S lenses you'll notice it in terms of AF performance and lose features like instant manual focus override. The 500mm D, IF-ED, AF-S lens and it's mid production run upgrade II version are AF-S lenses so they'll work with all modern Nikon DSLRs. Of course VR also came in as a later feature in the G series lenses which is part of why they demand such a high price. If you'll shoot primarily off a tripod with this big lens the VR might not be super important but if you'll try to handhold much you might miss it.
It really depends on your budget and your primary shooting interests. I owned and really liked the 500mm D IF-ED lens and it delivered great performance but did lack VR which can be nice in some situations. I would generally advise folks interested in action photography to stick with at least an AF-S lens (which this is). That said, my first serious long glass was the Nikkor 600mm f/5.6 P series manual focus lens and I loved that lens when I had it. It was completely manual focus but I still managed some action shots. though with nowhere near the success rate of my newer lenses.
Bottom line, you can't go wrong optically with any of the big Nikkor primes but from a features standpoint the G series adds VR and the E series substantially lightens the load and adds fluorite glass to the front element with a substantial redesign (the flaring front part of the lens). Are these changes worth the extra cost? Tough call and a very personal decision but if I was in the market for a 500mm or 600mm f/4 prime on a budget I certainly wouldn't hesitate to buy one of the Nikkor D series IF-ED AF-S lenses.
In terms of the Sigma Art, I haven't shot with that particular lens but do own a couple of Sigma Art series lenses and I've gotta believe it's a very good lens. But the price isn't so compelling that I'd necessarily take it over a similar used Nikkor lens in good condition.