There is absolutely no difference between cropping "in-camera" when the shot is taken or "in computer" later during post processing. Either way, you end up with exactly the same thing.
Well, I suppose there's one minor difference... with post-processing crops you can change your mind and undo it (or save the cropped version as a second file).
With in-camera cropping, you can't undo it later. Once it's done, it's done.
"Mirror" lenses like the Nikkor 500mm (aka "catadioptric") can be pretty good... it's possible the biggest problem you'll have with it is getting a steady shot. Even on a tripod, working from an 8th floor balcony there is probably some vibration occurring that will effect images. The image stabilization in the third party lens would probably counteract that and might make for sharper shots.
Years ago, I used a Tamron 500mm f/8 mirror lens that was quite good. Comparing them alongside each other, I was pretty certain one version of Nikkor 500mm was the exact same lens with a different rubber grip and, of course, different labeling. I had used a half dozen or so different mirror lenses and the Tamron (and Nikkor?) was certainly the best. Great color rendition, reasonably sharp and minimized the "donut" out of focus highlights. Both the following images were shot with the Tamron 500mm f/8 (on film that was later digitized using a Nikon L4000 film scanner)....
The image on the right ("bad hair day") can give you some idea how out of focus highlight "donuts" appear, with this particular lens.
I've also heard good things about the Canon FD and Minolta 500mm mirror lenses. Apparently there are also some good Vivitar Series 1 600mm f/8 and 800mm f/11 too. (Those were made by Perkin-Elmer company, which later made the optics for the Hubble Telescope, among other things.)
Konica, which I was shooting with then, never made a 500mm, but did offer a Hexanon Reflex 1000mm f/8... It just cost as much as a small car at the time! Konica also produced a 2000mm f/11 mirror lens, but never put it into production. Supposedly there were only two prototypes of it made and none were ever sold. The Konica "cat" lenses were unique in a couple ways. For one, they had variable apertures (most cat lenses have a fixed aperture, rely upon ND filters to adjust exposure). The Hexanons could be stopped down dialing a built-in, internal disk with "Waterhouse stops" into place. They also used a rear-mounted bellows mechanism for focusing on both the Hexanon cats.
Tamron also made a smaller, lighter 350mm f/5.6 mirror lens that was very good. It never sold in the same volume and is much less common than the 500mm, so is pretty rarely seen now and often sells for more than the 500mm.
There were two versions of the Tamron 500mm. The later one didn't have a tripod mounting ring. The earlier one did and that was the version I used. It was also quite close focusing for a 500mm lens.... as close as 5 feet, which makes for near macro magnification.
The above image also gives you some idea how the lens' f/8 fixed aperture handles backgrounds... in this case a fence that was about 15 or 20 feet behind the flower.
I usually used ISO 200 film (Ektachrome E200) when shooting with the f/8 lens. With other, faster lenses I used ISO 50 and ISO 100 films (Velvia 50 and Ektachrome E100VS).