Natural stone tiles can be beautiful but as a natural product they are less uniform in color and pattern, and require more planning for use and installation.
Granite or marble tiles are sawn on both sides and then polished or finished on the facing up side, so they have a uniform thickness. Other natural stone tiles such as slate are typically split on the facing up side so that the thickness of the tile varies slightly from one spot on the tile to another and from one tile to another. Variations in tile thickness can be handled by adjusting the amount of mortar under each part of the tile, by using wide grout lines that ramp between different thicknesses, or by using a cold chisel to knock off high spots.
Some tiles such as polished granite, marble and travertine are very slippery when wet. Stone tiles with a split surface such as slate or with sawn and then sandblasted or honed surfaces will be more slip resistant.
Natural stone tiles must be sealed and periodically resealed with a sealant in contrast to ceramic tiles which only need their grout lines sealed.
Most vendors of stone tiles emphasize that there will be variation in color and pattern from one batch of tiles to another in the same description and variation within the same batch.