Center groove down long board
It should be noted too that your success with using a table saw to run a center groove down a long board really depends on how straight and square that board is.
And, as everyone here knows, getting a long board straight and square is a challenge in and of itself. (At least it is for me. :))
Riding a router along the top, using one side of your piece as a guide for your fence will at least allow the router to follow along any long bow or cup in the wood and keep it more towards the center. Of course you lose the ease of set up with a table saw.