If you're purchasing only 1 of Heart Gold or Soul Silver, and you haven't decided which one based on nostalgia, the main deciding factor for which one you're picking up is usually the version exclusives. So far, it appears most people are leaning toward SS (at least based on the Media Create sales out of Japan), but should they be?
In the immortal words of Winston Wolf, let's not start licking SS's "popsicle" just yet. We need to do some math on this. So I'm going to rip off every sports series preview ever and go position by position trying to determine which game you need.
Early Game Bug (Spinarak/Ariados v. Ledbya/Ledian)
Spinarak and Ariados have one trick - trap-passing with Spider Web and Baton Pass, and passable offenses. Ledian has no offenses and no tricks beyond almost, but not quite unlike dying. If you're desperate enough to need something for Baton Pass, Ninjask is attainable in both games and learns BP on its own so you can pass it around. Advantage: Heart Gold
Fire Stone users (Growlithe/Arcanine v. Vulpix/Ninetales)
Arcanine is well known for having the highest stat total among non-legendaries/Slaking and for being the only true legendary dog in existence. It also has Intimidate which provides an auto boost to its Defense and a surprisingly variable ingame movepool of Fire move, Reversal, Crunch/Bite and Extremespeed. As much as I like Vulpix, its movepool goes Fire move/Extrasensory and a bunch of support moves, and no Intimidate. Advantage: Heart Gold
Red/Blue animals (Mankey/Primeape v. Meowth/Persian)
Probably the toughest call to make. Primeape has Sleep immunity or a 6 1/4% chance of opening up the proverbial 40lb box of rape, but Meowth gives Pickup and Technician and has most of the moves it needs to take use of that. Best to go with the sure thing in this case. Advantage: Soul Silver
Elephant or Bear (Phanpy/Donphan v. Teddiursa/Ursaring)
This is subject to change, as both families are in different games in the original North American games (Silver had Phanpy/Donphan, Gold had Teddiursa/Ursaring) but the original Japanese game and the currently available versions of HG/SS have it set with the listed arrangement. Ursaring is a pretty good Normal type with a sky-high Attack, but it's hard to argue with a type-bonused Earthquake from Donphan's attack. Advantage: Heart Gold
Major Birds (Gligar/Gliscor v. Skarmory)
Based strictly on ingame, unless you can hurl Gligar to another game to evolve it it's going to lose to Skarmory - less stats all around, despite finally being able to use Earthquake without an outside game Skarmory can do a lot of the same things, etc. If you can evolve it, Gliscor beats Skarmory. Based on that... Push
Minor birds (Mantyke/Mantine v. Delibird)
Mantine is a decently-powered Water type with insane Special Defense and a good HM compatibility. Delibird is Delibird. I don't need to say anymore. Major advantage: Heart Gold
3rd gen mascots (Kyogre v. Groudon)
Kyogre is one of the most dominant Pokemon in existence and it's consistently among the top used Pokemon in an anything goes environment. With auto-rain, that makes it a major team player. Groudon, although powerful on its own, can't hang with Kyogre. Advantage: Heart Gold
3rd gen freaks (Sableye v. Mawile)
If you want something with NO WEAK ZOMG~, get a Spiritomb. Sableye is going to be actively useless half the time, and only mildly useful the other half - whereas with Mawile, you get something with Intimidate or immune to it. Advantage: Soul Silver
3rd gen oddballs (Baltoy/Claydol v. Gulpin/Swalot)
This would be closer if it wasn't for the fact that SS essentially got a worse version of Muk, who isn't exactly setting the world on fire, Claydol is a shockingly versatile Pokemon with a lot of type variety and free entry hazard clearance. Advantage: Heart Gold
Exclusive without an event (Latias v Latios)
The attack and defense stats get swapped both ways, but Latias's Special Attack is still high enough that where Latios is KOing everything in one hit and dying, Latias is suriving those same hits and 2HKOing. I'll leave it up to the reader to determine which you prefer while actively encouraging you to grab the event and make this a moot point. Push
There's three other rivalries in play, as there's Pokemon easier to get in one version over the other.
Bug Catching Contest (Butterfree v. Beedrill)
Butterfree is a top-5 Pokemon ingame thanks to 98% accurate Sleep Powder. Beedrill... isn't. Major advantage: Heart Gold
Game Corner required (Ekans v. Sandshrew)
This isn't as relevant thanks to the Safari Zone expansions, but given a choice between a type-bonus Earthquake and potential Intimidate... yeah, gimme the Earthquake. Advantage: Heart Gold
Version mascots (Ho-oh v. Lugia)
Too close to call here, Ho-oh's massive offenses and 50% odds of burnination meeting Lugia's massive defenses and just usable enough offenses. Push
The final tally:
Heart Gold: 8 (2 major)
Soul Silver: 2
So yeah, if you want to make your life easier ingame, grab Heart Gold.