Well they're basically all the same from Gen III onwards, so this question is more "which mascot Legendary and/or evil team do you like the most?" because that's literally the only thing that changes from game to game. Evil team wants to use mascot legendary (or purple dragon that turns into giant hand for SnS) to rule the world. Protagonist stops them. The end.
I like Giratina the most, so I'm going to say Platinum.
I'll say Emerald. And for the reason why I'll have to cheat a bit; it's not the story itself, but rather one specific part of the story:
Right after awakening Kyogre when you return to the surface you're immediately greeted by the literal apocalypse. There's this constant change between heavy rainfall and intense sunlight, all the while there's this really eerie music playing in the background. It's a really powerful way to convey the massive power that Groudon and Kyogre posses and it makes you really think what'll happen if you let them continue fighting.
I'm probably gonna go with Platinum too, the story was pretty decent and I always loved having to traverse the region to the different lakes to thwart Team Galactic, it felt like we were on a proper mission! Emerald was a shout as well, mainly for that Rayquaza cutscene towards the end of the game lol
Gen 5 as a series I think had the best story, and I'd give the edge to the original Black and White storywise, even if I preferred B2W2 as a whole. I love the idea of Team Plasma being something that uses a noble cause to try and achieve their goals and has their lower ranks really buy into it, when in reality behind the scenes they are completely evil.
I'd say the Hoenn games, because I think they're the best at reconciling a pretty epic plot with a huge amount of freedom. Despite the plot being much more developed than in the first two generations, there wasn't much hand-holding and you also had a huge region to explore where you could find plenty of places and challenges that weren't part of the main story (like Pacifidlog Town or the whole Regis enigma).
it's gonna be black/white for me. i feel like it was a story that finally emotionally resonated with not only myself, but a lot of people. like there are other stories that are good and character arcs that are enjoyable, but i think BW overall had the best plot and character progression.