The pizza stone is certainly a better alternative to baking sheet. But due to the low heat development in a domestic oven (max. 250 ° C), it is then not the non-plus-ultra. I've bought myself a G3Ferrari pizza oven, the more than 400 degrees is hot and the results with this device are significantly better after just over a year. In addition, making the in the energy balance significantly more meaningful, because it heats up in 10 minutes at about 400 degrees, while the oven is on full level must Preheat up to 1 hour, so that the stone has saved enough heat.
On the grill, I have not used the stone, but can not imagine that it clearly makes more sense in a closed grill as in the oven.