I would have to pick the original KOTOR. The storyline was far more compelling to me than that of sequel, perhaps for the simple reason that I felt I accomplished something by the end of KOTOR. I identified well with the protagonist and I enjoyed all of the party members. They had backstories, quests, and personalities of their own that helped me to actually care about them. I found the darkside quests resonated with me powerfully. I actually felt strongly that my character's actions were deliciously evil. Unfortunately, I cannot say that I felt the same way about the DS actions in the sequel.
I suppose it boils down to a feeling of accomplishment. I got that from the KOTOR storyline but only confusion instead from KOTOR II's storyline. In fact, by the end of KOTOR II, I didn't feel like I had made any sort of major impact on the galaxy I had interacted with for several hours.
Why? I think it's for a number of reasons, but the foremost for me was that I believe the developers went out of their way to create something different. While they certainly accomplished that goal by my estimation, they sacrificed the basic structures that help to make an enjoyable game/storyline (deep characters, clear distinctions between good and evil, romances, a sympathetic protagonist, etc.) I also thought that the explanation for Revan's absence broke the suspension of disbelief for many players. I certainly had trouble believing the explantation as it was given. The missing content only helped to exacerbate the problems with the storyline that were already glaringly obvious.
For all of these reasons, KOTOR's storyline is the clear winner when compared to KOTOR II.