It's really hard to say as each person has their own preferences. (For instance with myself I'd say go for HGSS in a heartbeat, but others would prefer the DPPt line). I would say HGSS though if you played GSC (Gold/Silver/Crystal) back in the day and liked them.
As a rough comparison between Platinum and HGSS (you'd want Platinum instead of D/P because it's the better version - more content, improvements, etc) - Platinum has contests, 1 region, 8 gyms, gym leader rematches, Pal Park, safari zone, Battle Frontier, and a better trainer-rematch system as its main features while HGSS has the Pokewalker, 2 regions, 16 gyms, gym leader rematches, Pal Park, Safari Zone, Bug Catching Competition, Battle Frontier and the Pokealthon so they're pretty similar but HGSS does arguably offer more and what with the two regions - even if each region is slightly smaller than Sinnoh (DPPt's region) by themselves overall you have twice the Pokemon gym battles.
If you do have the money for it though I would suggest getting Platinum and one of HGSS so you have the best of both worlds! In the end they are both good really though.
So as you're likely get mixed responses (another thread asking 'which game did you get' has pretty similar results between all five games), I'm going to close. If you have any other questions please use the Help thread sticky at the top of this section.