PC: VR, wide selection of HOTAS, potentially much better graphics, occasional beta access, configuration options such as colored HUD and advanced graphics tweaks.
PS4 & Xbox: Honestly it doesn't matter between the two. I have a PS4 so I have the PS4 version. The xbox community has been around longer and so likely has more players. Vs PC, consoles have one thing in their favor: multiple commanders! You don't have to buy a copy of Elite for everyone that might use your PS4 or Xbox, anyone that has a user gets a commander.
PS4 drawback (maybe Xbox also, I don't know) You have to have a Live account. Well that's pretty standard for PS4 games so not a big deal, but it's a consideration.
Honestly, I think milligna is right that VR wins out for the PC. Once you try it, it's easy to get hooked.