I have both lenses and all teleconverters. I have found the 500PF quick to use. If I am traveling down a road in the Everglades and see something interesting, I am able to stop, and grab my 500PF already attached to me D5 and hand-hold the shot. If I am going to set-up in an area known for a particular species, I get the 600e and tripod/gymbal and attach my D5 then wait for some captures. If I am flying by air somewhere to do some shooting, I pack my 500Pf, a teleconverter and my gymbal monopod. I have not flown with the 600 or a large tripod. I like to travel by pick-up when carrying lots of photo gear.
I will add to your dilemma. I also traded a bunch of older photo gear and purchased a 180-400 Nikon lens. This lens has a built-in 1.4 extender and is becoming a well-used favorite. I like the fact that it uses the same internal filters as the 600e. I am able to use it hand-held and. when the world reopens from covid, I will include in some travel trips.
To summarize: if I had to keep one (what a foolish concept) of the lenses, the 600 e would be my keeper. The 600e has, in my photo experience, been an excellent lens with NO negatives. Big, yes, heavy, yes, needs a sturdy tripod and gimbal head, yes, but this is my passion.