One advantage would be that anyone who had eaten a particular dish cooked in the traditional manner would find that your dish had the exact taste and texture he remembered. For example, I have eaten baked beans cooked by my grandmother and my mother, and the taste and texture were slightly different They were the exact same beans grown by my grandfather, soaked in water from the same spring, flavored with the same type and brand of molasses, and baked in the same crock. The bacon was from a different source, The only other difference was that Grandma's beans were slow-cooked over coals in a hole in the ground, and my mother's beans were baked a little more quickly in an electric oven. Grandma's bread, baked in a wood-burning stove's oven until I was 12 or so, had a crunchier crust texture than did her later bread, which was baked in an electric oven. 'Better' is a matter of personal taste in these two cases; I'm just saying 'different.'
Some disadvantages of cooking the aforementioned beans and bread in the traditional way. 1.) Not everyone has a place to dig baking holes, neither might everyone who does wish to dig them, but every modern cook has a kitchen stove and oven. 2.) When Grandma baked beans, Grandpa dug the hole and dug up the beans when they were ready, and an older child usually saw to preparing the coals; that's three people who had to spend time preparing the beans, two more than my mother needed, and managing and moving coals can be a dangerous job. 3.) It is far more difficult to learn how to reach and maintain the exact desired baking temperature in a wood or coal-burning oven than it is in a gas or even an electric oven.
Some cooks are combining traditional and modern cooking methods. For example, you can bake chicken in terra cotta cookware, which does very nice things re flavor, texture, and juice retention, but you do it in a gas or elecric oven.