You'd be missing a lot of information to be honest since the sequel concludes Kat's story and answers a lot of questions from the first game. However, that's not to say the game wouldn't be enjoyable as 2/3 of the game has a more self-contained storyline, but the last part in particular is really a direct sequel to the first game. If you don't feel like playing the original game (which doesn't actually take long to complete), you should consider watching a playthrough or read up on the story of the original game and also watch Overture.
I've been playing the game since its release and, well, this franchise has really become one of my all-time favorites. It has unique gameplay, an imaginative world, an intriguing storyline, a brilliant soundtrack and a very likeable cast of characters. Only the camera is really something I found problematic at times, but it's a minor annoyance. I had little difficulty with the stealth missions so many reviews complained about. Not everyone will like it, but that's something that can be said about Panzer Dragoon as well.