I've never watched the anime passed the first 10 episodes. So the "anime" portion of the game doesn't matter to me.
>jesse and james
When they show up, I always forget about them. So they're like a bonus "surprise fight" just like the rival was on your first 1-2 playthroughts of red/blue. Very fun
>harder
bosses are better leveled, evolved, and move equipped. all around improvement
>different rival
I've played R/B so many times that's it's refreshing to not really remember what his team is about to be in the next fight. I also remember many time's "preparing" to fight his pidgeotto and getting a nice surpise instead... very good
>giovanni's sprite and his persian
These make him MUCH more sinister. Yellow's sprite of Persian may be my favorite of all... it's very clearly evil, and given how dangerous Persian was in Gen 1, there is a huge element of danger with him. Makes Giovanni much more threatening
>pikachu
when you box him, you actually miss the little fucker and that's annoying. however, he's still just a pikachu. i do usually nab one in R/B, so it's kind of handy having him given to you desu. That being said, i usually ditch him as soon as I have access to Jolteon.
>three starters
lots of fun to use all three. although i usually only end up using charizard, and that's just for his fly feature, really
yellow is awesome. i'd say it's the most fun and enjoyable gen 1 game, however, definitive is a stretch. it is, afterall "the special pikachu edition" which NO other title has ever recieved a similar differential. I think the main deterrent is the fact that you are given a starter. I think being FORCED to choose is a cornerstone of mainline pokemon games. It is supposed to be a monumental decision with costs and benefits because, ideally, you like all three... but MUST choose. There's some lesson in that.
If you wanted the "gen 1 experience" i'd say Red or Blue is the way to go. R/B is what started Pokemania.. not Y, Y was an afterthought