What do you think is the advantages of distributed systems over parallel systems? Parallel systems over distributed systems?

A distributed system's main advantage over a parallel system approach is the ability to re-distribute its different functions on to different platforms. That gives you the ability to both scale up (substitute bigger boxes for existing) and to scale out (add additional boxes that add same functionality).

A parallel system approach instead tries to concentrate on internal speed, which is nearly instantaneous compared to the latencies involved for a distributed system.