As far as I'm concerned, I don't think that Pokemon Platinum really has anything to do with Crystal at all, but in the same way they are alike. Here's what I mean:
Platinum is essentially the "Emerald" of the Diamond/Pearl series, since it's just like Diamond and Pearl, but with the following things:
-Focus on a specific rare character other than the previous two (Giratina is to Platinum like Rayquaza is to Emerald ololo)
-Inclusion of multiple Battle Buildings instead of just the Battle Tower (again, Emerald had the Battle Frontier, Platinum copied and pasted exact process but with less buildings)
-Updated sprites.
The only new thing that differentiates Platinum from Emerald (and D/P, for that matter) is that warped-dimension zone thing, which I haven't seen because I don't own the game.
Crystal shares this same concept, but on the GBC. Also, no Battle Tower. However, there are moving Pokemon sprites and the ability to choose between a boy or a girl, so... you know, it's a slight win-win there. ^_^
Yellow shares the same interesting concept. The only thing that differentiates this from those is the focus on Pikachu, lots of things from the anime, updated sprites and the Surfing Pikachu minigame.
So, in a way, Crystal and Platinum are a lot alike. Same goes for Emerald and Yellow, too. Maybe all Pokemon games that are #3 in a list share this concept? :D