Local stores are fine for top up items, but not for a big shop. It boils down to cost and choice and in bigger supermarkets there are more offers and choice. I also like to compare items and local stores carry less lines. I use them when a last minute guest comes over or if I need some fresh bread or eggs, otherwise I save more by stocking up at the supermarket.
On one hand , I do a lot of shopping at Walmart. On the other hand, I do buy my produce at the local farmer's market. So I'm both shopping at a corporate store and supporting local farmers. The one local family owned supermarket around here is really expensive and I'd rather support my family than theirs.
I usually shop at local chains, or more commonly, a regional chain called Ingles. They carry a lot of local products so I don't really feel bad about shopping there. Most of the money I spend there is going to go back into the local economy, so I'm fine with it.
Over here in my area, local grocery stores aren't common, so I have no choice but to shop in those large supermarkets that are also near where I live. We also have a lot of convenience stores too. I wonder if in the province I would have luck finding such stores.