The verbs "외롭다" and "쓸쓸하다" have almost same meaning when it is used to express someone's affect corresponding to "lonely". However, "쓸쓸하다" can be used to describe some place's atmosphere as well like "desolate". You can say "거리가 쓸쓸하다" (The street is desolate), but "거리가 외롭다" makes no sense, if it's not a poem.