New Super Mario Bros. is basically Super Mario Bros. but with different level designs, mechanics, and power-ups, so it's more different than it is better, presentation aside, allowing the original to still be appreciated as the things unique about it have held up.
Pokemon X/Y is basically Pokemon Red/Blue but better in literally everyway. More Pokemon, more features, more gameplay depth. Outside of nostalgia there's very little reason to play a lesser version of Pokemon.
You just contradicted yourself.
X & Y are basically Red & Blue but with different level designs, mechanics, and "power-ups". Yes, they are much better, but are still different games. You should have compared Red & Blue to their GBA remakes.
@OP though, if you really want to start off from the beginning to get a feel for how the franchise evolved, I'd recommend playing either Red or Blue, and then Gold or Silver. Which ones you choose, I guess it just depends on your tastes. I would post a list of the exclusive Pokémon of each version, but if you've never been into the franchise I don't think you'll have too much of a feel for any of the Pokémon so instead of it helping on your decision, it's only going to ruin a bit of the surprise of seeing Pokémon you didn't know.
I guess in the end, for a first-timer, it doesn't really matter which version you pick - just don't play both, since they're parallel versions for a reason (they're the same game). So, as I said, play Red or Blue, and then Gold or Silver. From then on, I wouldn't bother playing the other generations in order.
Edit: and about the Red & Blue hate, don't mind it. Red & Blue are still solid enough games and I'm sure you can find enjoyment in them - it's just that us Pokémon fans know that later games completely overshadowed the originals.