외롭다 means lonely, long term, related to solitude. 쓸쓸하다 means melancholy, short term, somewhat related to sorrow He's a lonely man = 그는 외로운 사람이다. 쓸쓸한 wouldn't suit here. I feel lonely = 쓸쓸하다. 외롭다 wouldn't suit here

They are almost the same.