First of all, neither of these are complete sentences. To make the first one a sentence you might say: Having just arrived from spending two years in Barcelona, I was fortunate enough to find a job. The second phrase could be written like this: I just arrived after spending two years in Barcelona.

The first one implies that you are going to say something afterwards or continue your thought. The second one needs the subject I in order to Make a complete thought that just states that you just got back from barcelona