The question I get most often is “What brand of running sneakers do you recommend?” The answer is complex because the band doesn’t really matter. All that matters is finding a running sneaker that best fits the arch of the foot and bio-mechanics of the ankle.
In general terms, 70% of runners have a medium arch and normal (neutral) pronation. Runners with high arches tend to under pronate and prefer narrow sneakers with cushioning. Runners with low arches (flat feet) tend to over pronate and prefer wider sneakers with motion control. All the sneaker companies make different models for the different types of arches and bio-mechanics. I recommend going to a running speciality store that has staff that will watch you run and/or look at your arches before suggesting what is best for you.
Personally, I have very low arches, but my bio-mechanics are close to neutral, so I look for sneakers that have arch support without motion control features. I like New Balance, Asics, and Mizuno because they tend to have a wider toe box for my flat feet.