Managed to solve my poblem thanks to this post (http://social.msdn.microsoft.com/Forums/vstudio/fr-FR/ab3c0cc7-83c2-4a86-9188-40588b7d1a52/processstart-of-xcopy-only-works-under-the-debugger?forum=netfxbcl) so actually the answer is:
This is a quirk of xcopy.exe. If you redirect the output, you have to redirect the input as well.
var command = "XCOPY ...."
processInfo = new ProcessStartInfo("cmd.exe", "/c " + command);
processInfo.CreateNoWindow = true;
processInfo.UseShellExecute = true;
// *** Redirect the output ***
// unfortunately you cannot do it for X Copy
//processInfo.RedirectStandardError = true;
//processInfo.RedirectStandardOutput = true;
process = Process.Start(processInfo);
process.WaitForExit();