TL:DR
It’s a bit complicated, but the gist of it is that Chernobyl was an RMBK-style reactor and thus lacked many of the safeguards and much of the shielding that the reactors in Japan (and pretty much everywhere except Russia) have. There is also the matter of different fuel types.
“This case is quite difficult, it would be closer to what happened in 1979 at Three Mile Island,” Rafael Arutyunyan, first deputy director of Institute for Safety of Nuclear Energy, Russian Academy of Sciences, said on Russian television. “Only a small amount of active particles made it outside and were released into the atmosphere, so there were no consequences for the population. That’s the way we’re heading at the moment.”
In short, the hazards are different, and while it is possible for bad things to happen to that Japanese plant, it won’t be like Chernobyl. Maybe Three Mile Island, but not Chernobyl.
I will say that hysteria will play a role here. If nothing else, very few people really know much about nuclear reactors aside from media hype. Who here knows what the control rods really do? I think that few people here even know the real reason that this Japanese plant is having the problems that it does right now, but it’s something so simple (to me) that I can’t help but facepalm. (It seems to be something that is not their fault, but more of a freak occurrence. We’ll see if it was avoidable :/) Bonus lurve for anyone who figures it out without looking it up.