Stone walls are often preferable over tile walls for a handful of reasons. First, there are no grout lines and without grout to clean, stone walls are easier to maintain. This means less time scrubbing, but also less opportunity for mold and bacteria growth.
From a design standpoint, stone allows for continuous veins and patterns, creating a more cohesive flow, a faster and simpler installation, and ensuring you get the exact look you desire.
Tile walls can be prone to damage. Cracking, chipping, and leaking are common problems. With stone, these concerns all but disappear.