One of the biggest differences in how homemade soap compares to store-bought soap is in the amount of synthetic ingredients. Typically, homemade soap is made from all-natural products while store-bought soap usually contains a number of chemicals and synthetic ingredients. Keep in mind, even though natural ingredients are generally viewed as being gentler on the skin, there may be some advantages to synthetic ingredients. These advantages include preservatives to make the soap last longer, exact controls on the strength of the ingredients and the fact that some synthetic ingredients are actually less irritating to the skin than some natural ingredients.
With store-bought soap you are limited to the options on the shelves, but with store-bought soap you can have your own custom soap made with your favorite scent, relaxing ingredients or healing oils. If you have allergies or sensitive skin, you can have home-made soap created that does not contain ingredients that irritate you. When you make your own soap you can experiment with different scent and ingredient combinations.
If you like a lot of lather and suds, you might want to stick to commercial or store-bought soap. Home-made soap tends to have a lot less lather and feels more like lotion-based soaps. On the other hand, homemade soap is usually less drying than commercial soaps that use additives to increase lather and make it easier to rinse off.