I love playing original tunes. As others have mentioned, your creativity is engaged. If I end up playing a really simple part it is because I decided, either alone or in consultation with my band mates, that a simple part would be musically effective. I never have to bow to anyone else's views though, we're equals when deciding what to play. Plus we come out of the jam band tradition, so changing things up from performance to performance is also fun, letting out chemistry as musicians really come to the fore.
I also really like playing one of our songs and knowing, when it goes over well with the audience, that *no one else* plays that song better than we do. Sure it's harder to reach people, so many people prefer to hear songs they've heard over and over before, but the people you do reach really respond and appreciate what we're doing. They get it, we're "for real" coming up with unique original music that they like.
I play in one original band and two cover bands (one does a handful of great original tunes though), and I appreciate the cover band thing. Often after a good set of covers, where the crowd really loved it, I tell my band mates, "It really wasn't fair, we played all of their favorite songs!" And it's true, I've had great responses to really mediocre sets just because they included some Led Zeppelin and Skynyrd. While I love standing on the shoulders of giants as much as anyone, I really love it when we do our own thing and it works.