The sneaker styles will provide some foot support, but they will raise the heel up about 1". They usually have deep traction tread, and are comfortable.
The slip on styles are less expensive, raise the heel up maybe 1/4", and offer minimal foot support. They do provide some traction and sole protection.
Like everything else, some trade offs, depending on what works best at that time.
Sport Cases (Electronics)
PFD's (Life Jackets)