Raised beds are not all that much different from growing plants in the ground so using a mix formulated specifically for containers is unnecessary and excessively expensive. Since raised beds by definition offer faster drainage than inground planting, just decent garden soil mixed with compost is more than adequate. Often bulk soil suppliers will have "garden" mixes available that are pretty much ideal for this purpose.

Typically the depth of raised beds for veggies is 10-12" but deeper may be preferred if you are doing more root veggies or things like asparagus.

It is important to remember that the restrictions that accompany growing in containers are not present in a raised bed situation, therefore the medium and the methods are quite different.