I like the storyline the first time you play, actually. This is probably slightly different than others. When you first see Malastaire in Marlybone, Newgate Prison, you know you want to get him. When you see Morganthe in the Azteca, Alto Alto Library, 3rd time, you know you want to get her. But you don't get either. That's why I'm always looking forward to what happens next.
Also, I like PvP. They really need to make it no treasure cards, though, and make the tournaments not cost anything. I just like challenging my friends at duels and seeing other people's strategies.