This! The Wire is a bit more authentic imo and doesn't rely on cliffhangers, action and dramatic sound effects in the same way many of the more recent series do. It's a killer show and the change of environment from season to season makes it more dynamic. Some find the episodes a bit boring but imo it's simply because the show reflects reality a tad more while being less action packed.
GoT is my favorite show nowadays. I'm fascinated with the story line, the environment and the acting is just awesome. I would probably watch that first if I were you but it's a win-win situation! Just make sure to have the other show ready for when you've finished the first one because if you really haven't watched them there is absolutely no time to spare!