As with Dutch Ovens, box ovens often are used for cooking on "car camping" outings. While you cannot (easily) hike-in a Dutch Oven to a remote camp site, you can transport a box oven folded up inside your pack. However, with the advent of Leave No Trace, the lack of an acceptable fuel source at most remote campsites has relegated the box oven in modern Boy Scouting to "car camping" where charcoal is easy to transport to the cook site.
I have seen some examples on the internet of folks using gas stoves with box ovens. I do not recommend doing so unless you are very proficient at using a gas stove and you are using a stove which permits you to regulate the flame.
Box ovens are easy to create and can range from the simple to the elaborate. They provide more air circulation than a Dutch Oven does and thus some cooks prefer the box oven for preparing cooked breads, fish, danishes, and pizzas. The range of items that can be prepared in a box oven is broad. However, many find that stews, thick meats, and dense vegetables are easier to cook in a Dutch Oven.
Try a range of recipes in both the Dutch and box ovens to develop your own opinion as to which oven best meets your needs.