What are the main advantages of using a model for concurrency based on processes over one based on threads and in what contexts is the latter appropriate?
Fault-tolerance and scalability are the main advantages of using Processes vs. Threads.
A system that relies on shared memory or some other kind of technology that is only available when using threads, will be useless when you want to run the system on multiple machines. Sooner or later you will need to communicate between different processes.
When using processes you are forced to deal with communication via messages, for example, this is the way Erlang handles communication. Data is not shared, so there is no risk of data corruption.
Another advantage of processes is that they can crash and you can feel relatively safe in the knowledge that you can just restart them (even across network hosts). However, if a thread crashes, it may crash the entire process, which may bring down your entire application. To illustrate: If an Erlang process crashes, you will only lose that phone call, or that webrequest, etc. Not the whole application.
In saying all this, OS processes also have many drawbacks that can make them harder to use, like the fact that it takes forever to spawn a new process. However, Erlang has it's own notion of processes, which are extremely lightweight.
With that said, this discussion is really a topic of research. If you want to get into more of the details, you can give Joe Armstrong's paper on fault-tolerant systems]1 a read, it explains a lot about Erlang and the philosophy that drives it.