A couple of years ago I picked up a Nintendo DSi with Pokemon Diamond on a whim, after seeing a massive billboard for Pokemon Platinum on the way to work. It just triggered this itch in me. Only logged 20 hours or so like (I struggle, I really struggle to stick with handheld games), but sill relived those glory days of borrowing friends GameBoy's for a crack at Pokemon Blue, which was amazing. I was sorely tempted by HeartGold/SoulSilver, but I think probably quite wisely I kept the cash in my wallet that time.
As for the 3DS, depends on the money you're willing to spend. I dare say that fundamentally, the games mechanics and such will be exactly the same. Except if you play on a 3DS you get Pokemon with bells on. Just think, 3D Pikachu kicking pokemon bottom in 3D. Either way, definitely upgrade at least to DSi. It has a wireless adapter, a Nintendo store and you can download an internet browser for free. You also get Flipnote Hatena, either bundled or for free through the store. That's a glorious hidden gem. Plus yeah, it is slightly souped up over the vanilla DS. And has cameras. What's not to like?
