And, much more is involved that just the waist width of the skis. The turn radius is important, labeled on the skis in meters, like 19 M or something. The smaller the number the tighter the turn at the same degree of edge angle.
The flex pattern is critically important. Some skis are made flexier than others of the same length and waist dimension. Some are more even flex, and some may have a softer tip and stiffer tail. And, in any line of skis, the longer the skis the stiffer they're made, with few exceptions. A flexier ski will turn more easily until it is overpowered by the weight or strength or speed of the skier, then it's a let down.
Generally the wider the skis the more float you'll get in deep snow. On groomers the wider skis take more effort to get on edge and put more strain on one's knees.
You know the difference in feel between a slalom snowboard and a powder board and boards in between those two.