Most hiking shoes or boots have EVA soles of varying degrees of stiffness. Some people hike in Five Fingers or other "barefoot" type shoes that don't even give you that.

I have found that for myself, hiking in mountains strewn with granite and roots and sharp slabs of rock sticking out of trails (never mind the cross country stuff), I do best with a somewhat rigid, but not totally stiff, sole. Asolo FSNs or Montrail shoes, and lately Trekstas, have been my usual. I have been going through a pair of hiking shoes every year or so but not everyone does 500-600 miles a year... The synthetic boots/shoes have a shorter lifespan than leather boots, but the offset is a lighter more comfortable shoe.

A good sole protects the bottoms of the feet from rough terrain. I like breathable shoes because my feet overheat. Since friction+heat+moisture=blisters, and my feet sweat, I try to remove most of the heat and friction - have not had a blister related to ill fitting shoes in four years. Fit is the other top priority when you are doing ten miles a day in the shoes. You need enough room in the toe box so you can tighten the laces and go down a hill without toe bang, and your heel shouldn't pop out as you walk.

I find that most hiking shoes/boots have pitiful insoles that don't last long. Replacing them with Superfeet becomes necessary after 50-100 miles or so. There are other brands of insole, some people find they need more arch or more volume.

Some of my SAR buddies have military boots, but they've worn them enough for their military career that they are used to them. Full boots don't work for me - the only damage I've done to my feet was in full boots, so I stick with mid height or trail shoes.

In other words, you have to figure out what works best for you, and the sole isn't the only factor. If you try on shoes or boots and they fit in the store, then go five miles in them and blister, they are probably not the right shoe. Unless it's a leather boot, which actually require breaking in - most synthetic hiking shoes do not ever "break in", they are as they are. I went through heck figuring this out due to my funky feet and a series of inept sales people. Hope you have better luck than I did.