This is one of the best TV shows ever made. Never watched the original, but I doubt it is as good as this.
The story, simply put, is this: We create robots that destroy most of us and the rest should find a way to survive. Sounds like a cliche science fiction. But it is so much more than that. Just watch the miniseries, the one before season 1. if you didn't like what you saw, don't bother trying to watch season 1.
This show takes place in a place million light years from our planet. There are 12 colonies of humans living in 12 different planets. Cylons were created by humans to guard the 12 colonies and make life easier for humans. The Cylons, as any robot in any fiction, rebelled against the Humans. eventualy, the war ended and they both came to an agreement and the cylons went to some other planet to start their own life there. The Cylons later began building Humanoids, Cylons who looked like them. 12 models were created and they went on to live among the humans and to somehow infiltrate their military defenses to strike again. Which they succeeded. Some people manage to escape the nuclear holocaust and later join up with the Battlestar Galactica. This is where the show begins and it gets better as it this is not your typical science fiction. There are social issues between the fleet and the military that the show deals with in a very realistic way. It never gets boring.
Even with all this, it is not the best science-fiction ever made. Fiction? yes. Science-fiction? no. The whole story is based on God and his plan for humans. The writer solves many of the issues with "god did it" explanation. It gets annoying a lot of times, but, if you are anything like me, you should be able to ignore it and accept it as fiction. I am an atheist, yet I found this show to be brilliant (excluding the lame explanations of impossible events).
The character development, the acting, the writing, the amazing twists and the directing is as good or even better than you could possibly expect from a TV show. And Bear McCreary's beautiful soundtrack adds a whole lot more to a brilliant show.