Soapstone will retain more heat and the hearth will be hotter - good for pizza but not necessarily for all baking.
Soapstone, like any material including firebrick will break should installed in such a way that it can be replaced. Set in sand/fireclay mortar with room to expand. Don't try a one-piece hearth.
Most ovens use firebrick. Some firebrick better than others. Can grind or sand edges to minimize chipping. Throw corn meal on surface to bake anyway.
Rod's oven has a hearth made with 12"x12" soapstone tiles. Some are cracked.
Soapstone would cost about $20/sq.ft.