The supermarket is obviously the most convenient place to shop because all of your fresh fruit and vegetables, meats and other essential items are all under the one roof. The upside of this is, you only have to visit one venue to get all of your household needs. The downside though, is more often than not, supermarkets are now located inside major shopping centres, therefore having higher rents to pay. High rents = high prices. Often there isn't as much variety to choose from because they carry so many other lines. Also, chances are you'll be able to buy fruit and veges that aren't in season because some supermarkets buy them in bulk and freeze them for later use. I don't know about you, but I don't fancy eating an orange that is months old.
The fruit and vege shop or green grocer, specialises in fruit and vegetables...of course. Now, buying your fruit and vege from a grocer will save you money because they buy their produce direct from the markets and will have a higher turn over. The produce will be fresher and the grocer usually passes the savings onto you. Beware though if your fruit and vege shop is located inside a major shopping centre...then you've got the high rents factored into your prices too.
The fresh food market is usually run by a wholesaler or directly by the farmer. As a producer or wholesaler, they can offer you the cheapest prices. You can find fresh food markets in most towns...whether it be the "first Saturday of the month" type markets or from a shop front (which is never in a major shopping centre). As a producer, they will offer you fruit and vegetables that are in season, so you'll be able to find produce that you normally wouldn't find in the supermarket. Yesterday, we came across 7 different types of potatoes alone, not just the washed or dirty varieties. The fresh food market may also have a meat and deli section, as well as dairy products, breads, sauces, spices, preserved goods, international foods and more. We are lucky that our fruit and deli carries a huge variety of products, at excellent prices.
I hope that helps you make a decision. Just by changing one thing in our shopping routine, we've already saved ourselves $100 in one shopping trip. For us, the choice is a no-brainer.