Martin kind of makes a point of depicting things as they would've been in a real medieval European society, rather than the sanitized kinds you'd often get in fantasy, and that involves extremely explicit violence as well as being more open about sex (though it's not like there's tons of it in the books - it's not like Jean Auel, if you know what I mean). In the case of the TV show, one of the most heard complaints is the really blatant nudity at times (someone even coined the word 'sexposition', after a handful of scenes in which characters have plot-advancing conversations with sex or nude women visible in the background).
But if you can get past all that, there are certainly very memorable characters and the plot twists are pretty brilliant.
Er. I'd recommend both series, but they're certainly very different.
The first two HP books (and movies) are definitely children's books, though upon rereading later you realize Rowling smuggled in a surprising amount of things that become important in hindsight. Three and four are kind of transitional, but certainly from the end of book four onwards things are pretty serious - they remain children's books in the sense that they aren't inappropriate for children, but become plenty deep enough for adult readers too.