The heat capacity of water is x5 higher than dry sand, gram per gram. The sand is more dense, x1.8, lets call it x2. So you need 2.5x as much dry sand to equal the same heat capacity as water at the same temperatures. The benefit of the sand is you can heat it far hotter than water, ie without a phase change. If you fill a set volume with water, and heat it to 95C (100C being the boiling point near sealevel) you would need to heat the same volume of sand about 2.5 times as hot to be the same energy storage. Any heat recapture system will need to be able to operate at these temperatures.
I played with some figures based on water - since I have lots of that, and it would be easy to move this heat around.
For a 100-million btu heating season, and assuming the water temperture needs to be at least 40C to provide any meaningful heating, the delta t is about 55C-degrees.
100-million BTU's /55C-degrees/ 4btu/degreeC = 454 cubic meters of water storage (120,000USGallons) if I had zero losses... so I cut firewood instead.