I am at a complete tie between SoulSilver and Platinum to be quite frank.
Platinum gave me so much enjoyment. And yet... so much irritation.
Breaking your chain when you get around 40 is probably the most pissed off you'll ever be, and I did that a thousand times over. I also spent well over an hour with most chains (at 40) running around, resetting the radar, running around, etc. until the shiny patch came up. Sometimes I'd ride that chain out for as long as I could before I either got sick of it, or accidentally broke it, catching as many shinies as possible with one chain.
But I also adored it's storyline and the Reverse World a huge deal. They were so well-done and amazing to me that I went through the game like 3 different times just to see it all again. I played that post-story like no other too. Battle Tower all day! >:3
SoulSilver has that nostalgic factor that's hard to beat. It's graphics are lovely and bright, the follow feature is adorable, and I found a ton of shiny Pokemon throughout my playthrough. I learned a trick regarding Secret IDs and Trainer IDs specifically for HGSS that kinda cranked up my shiny encounters. (Look it up if you want, you should find some info on what I'm talking about. Too lazy to explain right now. It might be some form of RNG manipulation, actually.)
My entire team ended up shiny by the end and it was definitely one of my most memorable playthroughs of all time. Also the Pokeathlon was so fun. :D
So ya know what? I just won't choose between them. They're both amazing and I'll pick them up any day to play again.