Mark, Jim & Gary,
Great comments. Many of the skis available are ideal for a certain style of skiing in a certain type of snow.
It's easy enough to find a good carving ski for firm snow. Select a ski with sturdy construction, a wide tip to aid turn initiation, narrow waist for quickness, deep sidecut to tighten the turn radius, enough camber to maintain edgegrip for the entire length of the ski; these features promote carving.
Its also possible (but not as easy) to find a a good crud & powder ski. Wide waist for float, narrow tip to avoid hooking of the tips, minimal camber to avoid tip dive, minimal sidecut to promote stability at speed and reduce deflection in crud. A powder ski depends on flex to determine the turn shape; big, and very fast skiers need a stiff ski, lighter skiers benefit from a less stiff flex.
The all-mountain midfat ski usually has the shape of a carving ski with a wide tip, deep sidecut and is simply wider. This reduces the skis agility and edgegrip on ice due to less edge-to-edge quickness and some loss of torsional rigidity. The ski has its limits in powder & crud also. The all-mountain midfat is less stable with more tip dive in powder and deflection in crud.
I know from experience that the all-mountain midfat models are highly versatile with sufficient carving potential on ice and more float in powder than a pure carving ski. The all-mountain midfat ski only works well because the skilled skier can adjust his technique to the conditions underfoot. On hard snow, the skier can carve well but needs to overcome some inherent sluggishness and less-that-perfect edgegrip. On soft snow the skier overcomes a less stable platform by increasing his effort or moderating the speed.
The real benefit of the all-mountain midfat is to transition from firm to soft to deep; all in the same run. But its a triumph of the skiers skill. It's not a triumph of optimized ski design.
Cheers,
Michael