처음 뵙겠습니다 literally means "I am meeting you for the first time," and you only use it when you first make someone's acquaintance. 만나서 반갑습니다 is literally translated as "I am glad we met" and can be used any time you meet someone, even if you have prior knowledge of that person, i.e. 다시 만나서 반갑습니다 - It is nice to meet you again.