There is a direct bus option from ARN to nearly the same spot (actually facing the train station) in downtown Stockholm where the ARN Express drops passengers off. It's much cheaper than the ARN Express and actually a few steps closer to the Sheraton Stockholm.

I find Stockholm to be a great walking city, and much better than Copenhagen at that. Stockholm is just not as "centered" (on one or two touristy "strips") and is not as tourist accessible as Copenhagen since it requires more walking to hit more of the spots and a little more research than CPH.