Online could be cheaper taking into consideration local transportation costs to the retail shop, less confronting, allows a more relaxed browsing time, a possible larger product range and more convenient. The downsides are longer lead times for deliveries and replies to questions and a less personable relationship with the suppliers. With online shops you are probably less likely to "impulse buy" as you have no immediate contact with the supplier to ask questions, though some online suppliers have active live chat facilities.
Retail shops have the "face to face" experience, which depending on your preference could be helpful or confronting. Prices may be more or less than online depending upon your local transportation costs. You probably have the opportunity to learn more about the relevant cuisine and experiment with new recipes. If you have a busy life style it is most likely to be less convenient offset by the fact that you will get immediate posession of your products. By purchasing from retail shops you are more likely to be supporting small business owners, though many online retailers are also small businesses.