I'm wondering which approach is faster and why ?
While writing a Win32 server I have read a lot about the Completion Ports and the Overlapped I/O, but I have not read anything to suggest which set of API's yields the best results in the server.
Should I use completion routines, or should I use the WaitForMultipleObjects API and why ?
You suggest two methods of doing overlapped I/O and ignore the third (or I'm misunderstanding your question).
When you issue an overlapped operation, a WSARecv() for example, you can specify an OVERLAPPED structure which contains an event and you can wait for that event to be signalled to indicate the overlapped I/O has completed. This, I assume, is your WaitForMultipleObjects() approach and, as previously mentioned, this doesn't scale well as you're limited to the number of handles that you can pass to WaitForMultipleObjects().
Alternatively you can pass a completion routine which is called when completion occurs. This is known as 'alertable I/O' and requires that the thread that issued the WSARecv() call is in an 'alertable' state for the completion routine to be called. Threads can put themselves in an alertable state in several ways (calling SleepEx() or the various EX versions of the Wait functions, etc). The Richter book that I have open in front of me says "I have worked with alertable I/O quite a bit, and I'll be the first to tell you that alertable I/O is horrible and should be avoided". Enough said IMHO.
There's a third way, before issuing the call you should associate the handle that you want to do overlapped I/O on with a completion port. You then create a pool of threads which service this completion port by calling GetQueuedCompletionStatus() and looping. You issue your WSARecv() with an OVERLAPPED structure WITHOUT an event in it and when the I/O completes the completion pops out of GetQueuedCompletionStatus() on one of your I/O pool threads and can be handled there.
As previously mentioned, Vista/Server 2008 have cleaned up how IOCPs work a little and removed the problem whereby you had to make sure that the thread that issued the overlapped request continued to run until the request completed. Link to a reference to that can be found here. But this problem is easy to work around anyway; you simply marshal the WSARecv over to one of your I/O pool threads using the same IOCP that you use for completions...
Anyway, IMHO using IOCPs is the best way to do overlapped I/O. Yes, getting your head around the overlapped/async nature of the calls can take a little time at the start but it's well worth it as the system scales very well and offers a simple "fire and forget" method of dealing with overlapped operations.
If you need some sample code to get you going then I have several articles on writing IO completion port systems and a heap of free code that provides a real-world framework for high performance servers; see here.
As an aside; IMHO, you really should read "Windows Via C/C++ (PRO-Developer)" by Jeffrey Richter and Christophe Nasarre as it deals will all you need to know about overlapped I/O and most other advanced windows platform techniques and APIs.