both are correct. but first one seems more polite and honorific. so when you meet an older person, you can use it. 반가워요, it sounds friendly. when you meet a younger or a same age person, use this one. you can also use first one in this case, but if you want to look a socialized person, 반가워요 is better. Please don't use it in front of order people. maybe they think you're rude or an overactive person.

Hmm i make a guess but i cant promise it is right. First of 마나다 반납다 in "만나서 반갑습니다 " are both verbs. The sentence has the 5th level of politness. The verbal suffix 서 marks the cause (temporal or reason) through that it becomes the meaning of "because we meet" 반갑습니다 "i am glad" .. so it is like "I am glad because we meet" or "I am glad that we meet" .. and this in a very fromal way. Also I dont know 반가워요 ..you can already see that this is the 4th level of politness and maby ! therfore more commenly used if you talk to people that arent like over 60 XD.