One additional item to consider if your going to use this lens for wildlife photography. And that is neither of the two lenses you listed have the newer electronic aperture control. But the Newer Nikon 200-500 does.
So, why is this important. The new electronic aperture control allows all of your exposures to be consistent when shooting at a high frames per second. With non electronic aperture control all exposures in a sequence may not be the same, and this can be unnerving for a once in a life time moment.
This is yet another reason to consider the New Nikon 200-500. Which actually comes in between your two lenses on price, and the 200-500 would be new and comes with a 5 year warranty. Just sayin.
I have used all three lenses for an extended period of time and yes, the 200-500 is the clear winner.

Or put a different way, $1550 vs. $552. I'm trying to decide which lens will be best for nature photography, especially birding (on the wing).
Roberts Camera's used supplier has both lenses at the price mentioned, both in excellent condition. I'm just not sure if the $1000 difference is going to give me that much more in regards to faster focus and better/sharper image quality.
They both have Vibration Reduction but the AF-S lens is a half pound heavier than the older model, and I do a lot of hiking where I typically don't use a tripod.
Sure could use some guidance from those that have experience with these two lenses to help me spend my dollars wisely.

Within a year of buying my first ever camera (1980 - Nikon FM) I was a full-on photo fanatic. Friends saw this and asked me then, had I not bought the Nikon, what camera brand/model would I have rather bought.
We have a number of other "old-timers" here and I was wondering if any have pondered this question themselves. Back then, what 35mm format camera would you have bought if money was not an issue?

For me, at the time, I had a huge "crush" on three other cameras, curiously all with German ancestry. My choices were: Rollieflex SL35 E, Contax 167MT, and Leica R3 Safari.

Luckily for me, I didn't know anything about any of them at the time I bought the FM. All of those companies went out of the camera making business some time back. Thank-you, Nikon, for hanging in there.