Legendary? Dark? Lightcore? 2nd Ed? What?
Solution 1:
Legendary/Dark variants of characters have different stats than their "normal" counterparts. Legendary stats start and end a bit higher that normal versions, Dark stats seems to be just distribute differently. Color variants (gold/transparent/glow in the dark, etc.) seem to be the same as regular versions, I'm not sure the color differences reflect in game at all.
Series 2 figures of characters already available for the first games (otherwise known as "re-posed") are identical in stats and usage between games, however, they have extra abilities available in the 2nd game, called Wow Pow upgrades, so if you have a choice between buying a 1st or 2nd series variant, I'd get the 2nd.
Lightcores are compatible with the first game (if the non-Lightcore character was in the first game), although it states on the packaging it isn't. I've tested this personally with Lightcore Drobot (illest of the Skylanders). I couldn't find online if there's stats difference between Lightcore and normal versions, there are Lightcore only abilities, though, so it's possible.
I cannot tell how Skylanders leveled higher than 10 behave when placed back in the first game, I assume they'd still be capped at level 10 and new "Giants only" abilities/hats will be unavailable. This is just my assumption.
Here's a nice handy chart detailing character/item compatibility between the games (like stated before, the Lightcore incompatibility isn't true):
Solution 2:
The 2nd Edition figures, Cynder, Chop Chop, Slam Bam etc also have a new upgrade in the shop. Its called a Wow Pow and it seems its only the repeat characters that have it, it will add some new or alter an existing power.
Ignitors is called Blue Flame! and chages his flame form to blue flames and leaves a trail behind him