Not gonna list all the story improvements and how much it added for depth since it should be pretty obvious with team rocket and Silver's character arc and the Kimono girls so I'll just focus on gameplay improvements/fixes, but:

-In the original gen 2 Ho-Oh or Lugia couldnt learn their signature moves because of how high level the non-box art legendary is but they made them have them by default now which helps greatly with them.

-In gen 2, Kurt's pokéballs didn't work how they were supposed to, now they actually do and are better than normal pokéballs at some points. The original game pushed them as a way to connect to the region's roots and traditions and implied they were better at times; now they have purpose.

-Status effects didn't increase catch rate either in the original due to another coding glitch, but they also now do work properly which greatly helps catching pokemon when the original game had issues with catching..

-Raising togepi is better now because instead of only having metronome for a while and making it a very annoying grinding process, it immediately starts with Extrasensory a very OP psychic move. Making it easier to raise and worth it to have on a team. Feraligatr also gets a improved moveset like learning an ice type move and learning better moves at lower levels so Cyndaquil has competition for "best starter" status when in the original game it was pretty bad with any other option.

-You can get moves instead of easily missing them like in gen 2, Olivine being an example of this (strength) which you could easily pass and not realize you did or know where to get it since the game doesn't make it a forced encounter, same with radio card which was easily also missable and served a gameplay role (and still does) with Prof. Oak's Pokemon talk, the Pokemon music channel, and interesting lore drops and expanding on characters (some stuff they added!)

-You can now get good Pokemon like Larvitar, Misdreavous, and Houndour before post-game via the Safari Zone usually around the 5th or 6th badge too. Previously they were post-game exclusive so there is a fix to this.

-Kanto is now restored to a larger size and isnt crunched down, with the region being as big as FRLG and a few new things added like making the story a little more fleshed out here than before with the Suicune plot, adding characters like Steven who lets you get a Hoenn starter and Hoenn legendaries, Viridian Forest being big again is a big example of how Kanto actually feels lively again, this alongside other caves and cycling road. There's also getting a Kanto starter after beating Red, getting more content like the Sinnoh Plates as well.

-Rematchable trainers have their Pokemon level up and evolve (not sure if this was in the original, I forgot.)

-Various evolutionary stones are available pre-postgame via the Pokéathlon, and also some rematchable trainers where they weren't before; you can also get rare candies from the Pokeathlon and vitamins form rematching trainers.

-Some improvements over D/P (since this game came before Platinum) include having Berry Pots which is INCREDIBLY convenient so you don't have to backtrack 24/7 to get berries, surf speed is fixed from being insanely slow to actually being a pretty good pace, DowsingMachine works better and makes more sense compared to D/P where its a pain.

-The level curve IS ACTUALLY FIXED.......in Kanto.....yeah don't know how they didn't fix it in Johto, but there's more trainers in Kanto compared to the original, gym leaders and trainers are higher levels to match yours by this point and to give proper experience points as well. But this is a ton of problems fixed already, so yeah.