As Totalgit mentioned, unique characters (named characters from the book) tend to be stronger. If you like Stannis, Robb Stark, Tyrion, etc. then you're likely to be able to build a deck in which those characters perform very well.
Three caveats. First, this is true for some houses more than others. Baratheon is great in that you can build a deck with most of your favorite characters that is competitive. Stark is pretty good too, though certain less prominent characters (Meera, in particular, but also Shaggydog, Reek, etc), are stronger cards than what one would normally consider the important characters (Arya, Eddard, etc.). Lannister is similar to Stark in this respect, whereas Greyjoy, Martell and Targaryen all tend to be quite a bit different. You won't see many competitive decks built around a single character from the books, with perhaps the exception of The Red Viper, which is one of the best characters in the game (from any house).
The second caveat is that if you like Khal Drogo or Jon Snow, then chances are you like the dothraki or the Night's Watch themes. In general, thematic decks in this game are not competitive. So while Khal Drogo himself is a great card (and there are several different versions all worth experimenting with), a deck focused on dothraki more generally falls into the "fun but not realy competitive" category. Same is true for other houses…decks built around House Tully/Riverrun, House Dayne/Starfall, and even "Kingsguard" tend to be as uncompetitive as they are thematic. There are a few traits, such as Clansmen and Dragons, that show some promise and in certain cases may be very competitive. But as a general rule, the more cohesively thematic the deck is, the less competitive it is.
Lastly, while you'll see a decent number of named (unique) characters in play, the non-unique characters (cards like IG86droids) still typically make up about half to 3/4 of character cards you play, or roughly 1/4 to 1/3 of the deck itself. Of course, this depends on the house or build of deck that you are playing. But in this game characters are constantly dying, and typically you need a good number of generic characters to fall on their swords throughout the game to keep your named characters alive. Each house has at least one non-unique card that seems overly powerful though, and at times it can be annoying if you're getting beat down by the generically named Wintertime Marauders or The Conclave. But overall, unique characters tend to be more powerful.