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.

You may want to read a review that compares all but the G2, to better inform your decision:

https://photographylife.com/reviews/nikon-200-500mm-f5-6e-vr

You can dig around the web a bit and find a review that compares the G2 to at least one of the others. You'll likely come to a similar conclusion - that the come away winner in image quality is the Sigma Sport, and if you compare the Sport to the G2, you'll find that they are very similar in image quality.

The problem with reading suggestions here, while well-intentioned, the posters may not have the experience with other lenses - and have made a selection based on their own needs, and naturally love their choice and will rigorously defend it. But that can be biased. Or they will take the form of "if you have Nikon bodies, use Nikon lenses - as if Nikon lenses ALWAYS perform better than the competition. I personally have owned over 30 lenses in Nikon mount, and a third of them are not made by Nikon. I'vefound the Nikkors for Nikon rationale to be a bit of an urban legend. In the review I posted the link to, it shows that the 80-400 AF-S was not the best performer, and that the 200-500 was quite good, though not at the level of the Sigma Sport. I personally came to that conclusion before even knowing about the article, having borrowed/tested all of the contenders at the time (the G2 was not available then).

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.

You have made some excellent points especially around members fiercely defending their own choices and assuming their decisions are right for everyone else. I would like to add my experience with Nikon bodies and Nikon, Tamron and Sigma glass to the discussion. You have to carefully research who makes the best lens for a specific purpose. For example, Sigma makes a better 50mm f1.4 lens than Nikon does and both Sigma and Tamron make better 35mm glass than Nikon per DxOMark. There are cases where Nikon makes the best lens hands down like the 200-400mm f4G, but you will pay for that quality. Tamron and Sigma are a much better value for similar quality AS LONG AS YOU ARE WILLING TO TUNE THEM. If you are not willing to learn how to, and actually do tune them, then buy Nikon.

I've never tuned my lenses - or camera bodies. If I suspect something is awry, back it goes for repair/replacement. I have too many lenses and have used too many camera bodies to consume my time paying attention to stuff like that, when the technicians can do a better job, have better tools, and can be far more granular in their adjustment capability. I need consistent interchangeability from body to body - if I can't get that, I return the lens. Buying Nikon does not ensure that it will be perfect either. I have a 600mm F4 that would not focus on a new body. I took the lens and body (and another body for illustration purposes) to Nikon, and they wanted to adjust both the body and the lens. I refused to let them touch the lens, since it was working just fine on my other bodies. They complained but did as I asked. They adjusted "communication parameters" in the body and when I picked it up is was perfect. And they did not cheat by using a lens specific profile in the body. All the fine tune data showed zero - no adjustment.

Otherwise, I totally agree -

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.

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.