Except it didn't. The first part did. Once John Connor is rescued and he figures out what is going on, he becomes proactive and seeks out and rescues Sarah. That's not really a chase sequence. And then they are safe, until Sarah seeks out Dyson to kill him, and together they seek out the labs to destroy those. For most of the film, the protagonists are not merely fleeing or being chased, they are proactive and following their own agenda. It enRAB with more chasing, but the balance over-all is much better.
It has more soul than the first film, partly because of how it develops Sarah's character, and because of John learning to be a leader and Arnie learning to be more human. There's so much more going on than in the first film.