I think it totally depends on your particular foot/knee/back needs. I run on a treadmill, but my running sneakers torture my arches if I wear them at WDW. Strangely, the less supportive the shoe, the longer I can go in it. In the past, I wore the thinnest, squishy flip flop I could find or Converse All Stars. And I'll always switch shoes halfway through a long day at the parks.
But I just got my first Crocs and may have found my dream WDW shoe! We'll see...