Which option would work better for moving rain water off my property?

I built a patio extension in my backyard which created a small problem of water building up around the foundation. There are three gutters also installed on the edge of the patio extension. I initially thought of installing some underground drainage and catch basins to move the water.

I had a land grading contractor to come out and he said that re-grading the backyard might be a better and cheaper option because the backyard is sloping slightly towards the house which is enabling the water to build up and hold around the foundation. He said he could re-grade it so that the rain water will flow out to the edge of the property line where a drainage ditch is located. He also recommended installing a rock bed going around the perimeter of the patio extension.

So, my question is which one will serve as the best solution, the underground drainage or re-grading of the back yard?