There's no one answer that's right for everyone and every area. Rock isn't going to do anything as far as letting water run off. The water is just going to go right through the rock and then through the landscape fabric, which is permeable.
Advantages to rock: You may like the way it looks and it's available in wide variety of types Doesn't require periodic renewal No termite issue
Disadvantages: Over time, dust, debris, wind blown dirt, leaf debris, etc will accumulate and some weeds will still manage to grow. When you want to add/remove a plant, it's a pain because you have to ty to pull back the rock, not get soil in it, etc It's not good for plants, particularly in hot, full sun environment
Advantages to mulch Retains moisture, better for plants Easier to work with when adding/removing plants
Disadvantages: Has to be renewed every few years. Possible terminte issues
Personally, I've had both and tend to prefer mulch.