I used to work at Stride Rite and am pretty familiar with their products. I also now have two children and buy shoes for them. To me the benefit of Stride Rite shoes, over those you can buy at Payless or similar stores, is the wide variety of widths, the quality leather, and the staff who helps measure the foot both for length and width. Little feet do better with soft, breathable leather. Even leather shoes sold by Payless, etc. are not usually as soft as the leather used in Stride Rite shoes. Perhaps even more importantly though, children need a shoe that fits: one that is not too narrow and constricting or too wide and floppy. So whether you buy at Stride Rite or go "cheap" make your first priority a good fit.
Personally, I take my children to Stride Rite for a fitting every few months, just to make sure they're wearing the right size. I usually buy one pair of shoes there, the pair they wear most often. Then, I typically buy church/special occasion shoes and a pair or two of "knock around" shoes at some place like Target. That keeps the cost down (which in turn keeps my husband happy) and I don't worry about what they're wearing.