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What is the difference in cognitive effects on the user between simply showing that there are 'some' unattended notifications, or showing how many notifications there are?

Take Facebook's notification count for example, Facebook's notification count

as opposed to Windows' PC issues notification Solve PC issues tray icon in the system tray.

Of course depending on what the notification is notifying you of, people will respond differently, which is not something I'm interested in. However, I suspect there could be a difference based on where it is being displayed, e.g. whether it is always visible or not. Would one be preferred over the other in different situations?

I'm mainly interested in a comparative study between the two, but any research which might give additional insights in the two separate representations would help me out as well.

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I found a related question on UX, but let's see whether we can do better here! –  Steven Jeuris Sep 12 '13 at 14:54
Just very practically: I work at my computer and don't want to deal with unimportant email, but still want to be available for important email. My mail program displays the number of unread email in the "Dock" (on a Mac). Now, if I look away from the screen for a few minutes (e.g. to read an article) and then look back at it, I can see if new mail has arrived. If it has, I switch to the email program and check if it is important. Without a number I'd have to regularly check. (The sound of my computer is turned off so as not to disturb my colleagues, otherwise the "ping" would notify me.) –  what Sep 12 '13 at 16:56
@what You mean you remember the number then and see whether it increases? –  Steven Jeuris Sep 12 '13 at 19:51
Yes. @StevenJeuris –  what Sep 12 '13 at 20:37
@what Never thought of it that way. Already useful input, thanks! The question remains though. Suppose it would always show the amount of items you haven't 'inspected' yet, or just an indication that there are some you haven't inspected yet. –  Steven Jeuris Sep 12 '13 at 21:04
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