I must say yellow is my favorite game, and I'm so disappointed they haven't polished it in the Advance generation.
First of all, it's really great having all three starters without having to trade from other games. Sociopaths like me who play alone don't have to buy multiple GBs and cartridges to get Venusaur, Charizard and Blastoise. But sure, trading is better as you get all three from level 5 instead of 10.
But the unique thing is having a Pokémon following you everywhere, being able to check on his mood and going to battle without the ball animation (Pokéballs taste a little like tiny cages). I would have liked to see those things rendered in a modern engine. Also, having a badass electric attack like thudershock from the beginning is rad (let's talk about training with all those Pidgeys and Spearows at the start and Zubats in Mt. Moon, plus obliterating Blue's second Pokémon Spearow and Misty's gym).
Never watched nor liked the anime, but also without enjoying the similarities between the two it's still my favorite Pokémon game.
Sure, it would have been nice to see Raichu's sprite following you, or his face expressing his mood. Also, evolving would have made it even stronger, making more probable to let it in your team and have its sprite following you forever, but the fact that it refuses the stone makes that Pikachu more unique, so it isn't a huge bother.