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Not really. The main advantage either game has is connectivity, with GSC having RBY/Stadium 2 and HGSS having [essentially the entire rest of the series], but especially DPPt and PBR.
Assuming real hardware, the main advantage to playing the originals over the remakes SHOULD be accessibility (last I checked they're expensive but not HGSS expensive), but due to the RTC draining the battery extra fast, you'd need to actually replace the battery in any old GSC carts you find, assuming the seller hasn't done that for you. IMO, if you really want to go about playing GSC on real hardware, you should make your own Reproduction carts or get a Flash Cart instead. There's actually a board out there now that can save the game without using a battery backup, but does still support a RTC battery, and when the battery dies your save is fine and it doesn't need soldering in a new battery to fix it, because the battery is actually removable (pic related). If you don't, the battery is just going to die *again* in another 7-8 years.
If you're just emulating, though, play whatever.
