I decided to bring my New Balance only, along with a pair of flip flops for the pool, and I deeply regretted that decision. These weren't new shoes, and I had socks I could breath in and everything, and my feet were COVERED in blisters and in so much pain, I finally gave in one day and bought a pair of Crocs flip flops at EPCOT, and it was the best thing I did for my feet! I actually wore them the rest of the trip b/c they were so comfortable, and gave my feet a chance to rest and heal. So I say whatever you do, bring at least two pairs of shoes so your feet aren't being pressured in the same place every day.
On a side note- the WORST shoe decision I ever made in my life was in WDW. I was 17, on our Senior Trip, and too concerned about being cute to worry about comfort. So I brought a pair of jelly HEELED shoes I insisted on wearing...and ended up having to be carried back to my room at the end of the night. And this wasn't my first rodeo at WDW. KIDS!