What is the difference between Process builder and workflow?
A pretty complete overview with examples of which automation tool to be used in which case can be found here.
In short, you can do everything you can do with workflows using process builder as well, except for sending outbound messages with point&click. With process builder, you can also update all child records starting from the parent record, which is not possible with workflows (only vice versa is possible using cross object field updates). I've heard rumors that process builder will replace workflows in the future, which seems a logical step to take for sfdc.
However when you compare the execution speed of workflows and process builder you'll find that workflows are incredibly time efficient. Whenever you can use a workflow instead of process builder you absolutely should.
I completely agree with @Venko. Process Builder is powerful, but in my experience it's still unreliable. When Processes crash, debugging the cause is nearly impossible. To make matters worse, sometimes they crash for no apparent reason at all, and that crash will stop Triggers and other custom logic from working. Performance is a definite concern as well. I recently analyzed debug logs for a client that was seeing 20+ second delays when saving a record due to a series of Processes their admin built.