Tough to say. HeartGold's definitely got a lot going for it, but so's Platinum - it's basically what DP should've been (then they could've just had 4 games in a Gen, like Gen V).
I don't get the title of this thread though "which game to start with". If you haven't played them, go for Platinum. About the only things you'll miss out on from DP are Stunky and Glameow, which plenty of people on here would give you I'm sure.