>>57913323HGSS are my personal favourite in this regard. Kanto alone is very pleasant to explore but aside from that, I have an option to focus on other activities like Pokeathlon, Battle Frontier and Safari Zone. Meeting gym leaders outside to collect their phone numbers and later battle them is a great addition too - it makes the game's world more lively.
BW2 would be my second pick. They offer a lot of areas to explore allowing you to see what changed after BW1. Additionally, finding strong trainers as well as legendaries is fun and I actually really like World Tournament and White Treehollow/Black Tower. They are much more interesting than Battle Frontier.
DPP and BW are good for similar reasons. I am really fond of an idea of traversing new places after credits.
FRLG have Sevii Island and I like them as well but they are inferior to DPP's Battle Zone or BW's postgame Unova.
SM don't really expand Alola much after credits but you can find out a TON of new stuff if you go back to previous locations. The game's world benefits greatly from it.
XY are relatively poor in terms of postgame content but I like Looker's storyline. ORAS are better - aside from postcredits storyline, you can focus on collecting legendaries, winning contests, playing more with secret bases and finding out some optional stuff (e.g. meeting Winona on top of Mauville).
GSC have additional (even if simplified) region to explore so I like their postgame.
I don't care about RSE and RBY postgames. Battle facilities get boring fast and Cerulan Cave is suffering to explore.
Yea, I know some of the stuff listed is not postgame exclusive but I don't spend dozens of hours on Pokestar Studios or Pokeathlon in the main game.