Both lenses are great, but they serve different purposes in my opinion.
First, though - sharpness wide open. The 600mm is better along the edge areas, but in the "business" area of the frame I can't really tell my 600 E from my 500PF. Plus, both lenses are weather-sealed really well, are fully featured with function buttons, and in my tests AF speed was the same.
Also, the 600 + 1.4 TC is 840mm
The 600 F/4 is going to give you another stop of light of course, and that's huge - it can sometimes mean the difference between having enough shutter speed to get the shot or not. When I use the 500 PF, it always seems like I'm running into ISO and shutter speed limits, the 600 F/4, not so much. The F/4 also gives you better TC performance. Not only is it a stop faster than the 500 PF + 1.4, you can also still use all of you AF points as well. At F/8, even the best cameras only have 15 points that Nikon says are reliable and only one (the center) is cross-type (and that's even on the D6). If you're planning to use TCs, this is a big deal. When I was reviewing the 500PF, I actually stopped using the TC due to poor AF performance on my DSLRs - and F/8 is tough to swallow when you're in dim conditions.
F/4 also delivers better subject separation than F/5.6. It's subtle difference, but it's there for sure. I also tend to agree that the 600 F/4 has better bokeh as well. For my photography, backgrounds are just as important as the subject -
so much so I'd list background separation and bokeh as my primary reasons for owning F/4 glass!
For me, the 500PF is great, but it's more of an addition - not a substitute - for faster glass.
All that said, you also don't want to underestimate the flexibility you get with the 500PF. The lens usually doesn't need a tripod, is easily hand-holdable, and can allow you to maneuver more quietly than a large lens / tripod / camera combo can. I'm often able to approach closer with the 500PF than I can with the 600 F/4. And the 500PF is just more fun to shoot too!
Still, if I were in your position and needed to choose, it's not even a contest - 600 F/4 all the way.