I'm just going with the more supernatural aspect, as the realistic aspect would be, to put it bluntly, a bit boring since it would just be a bunch of kids playing with cards and 'competing' with each other. Truth be told that's not much of a story. I did read a series about a card game/board game and how it linked a faerie world with the real world while the cards served as information, so they were like a cheap version of the PokeDex and a helluva lot more inconvenient. In any case, a supernatural feel would give the story more room to work with versus a realistic approach, which I think would be incredibly hard to come up with a decent plot for. I don't know which you prefer, but I'd just say go with whatever gives you more ideas, because then you'll have enough space to do anything. With that, I think a fantasy-mix would work better because there are a lot more things that could happen in that sort of universe while a straight TCG would be just TCG and would seem, to me, more thematic or symbolic.
Kinda depends on what you want to go for and what you can produce. That's a terrible way to put it, but eh.