I will be able to try both at some point, although I'd like to start with some thoughts in place along with an open mind - clearly there are pro & cons.

I like motor sports and air shows, and would like to spend more time on wildlife. I'm very much an amateur, taking photos strictly for my own pleasure. Disappointingly they are mostly snap-shots, occasionally very well timed, obtained at considerable expense. On the positive side, by buying unnecessarily expensive gear I contribute to keeping the costs down for everyone else, but that's a different topic;)

Although the 80-400 doesn't have quite the reach, cropping an 850 image should still yield decent results.
It is smaller & lighter, and means I could possibly dispense with my 70-200/f4. Maybe. Years ago I had a Canon 80-400 L series which was superlative, but it sucked in a lot of dust and didn't quite have all the reach I would have liked.

The 200-500 has a lot of reach and is less expensive, but is big enough that it would only be used when really needed. Probably not something you're going to leave on the camera for "just in case".

Thanks in advance for your thoughts and comments.

I am about to lose my travel laptop. Old, like me. I have searched here on the Hog for suggestions. They seem to be dated and as technology moves forward so quickly, I decided to ask this amazingly informative group for suggestions. I use LR and have a desktop (PC) for my post processing and I want to fully work on my photos when we are wintering elsewhere. My budget would be about $1300. I have been looking at Alienware by Dell and Lenovo Legion y520. I would like 32 GB ram, 512 SSD and 1-2 T HD i7core. But graphics card and such, I would like advice. I have looked at some of the sites suggested for “make your own photography laptop” but they are so expensive. And I am not sure I need it all. I will be switching to the Adobe subscript LR/PS when this is purchased. Should I get an external HD to put catalog and photos on to for transfer to home PC? Thank you ahead of time for your assistance. BTW, I travel to a lot of the National Parks and carry a Nikon D750 with some good glass.