Both are correct. Which to use would depend on how many advantages there are. If there is one advantage - you would say "The advantage...". If there were several advantages, but you were mentioning one of them, you would say "An advantage..."

Both are correct, but they have slightly different meanings. "A" and "The" give different meanings, as you probably know. An advantage (=any one of many) of ... is that ... The advantage (=the main or only one) of ... is that ... "An" refers to any one of several - it is general and vague. "The" refers to the main one, or the only one - it is specific.