With traditional display media, CPM is often more used for branding purposes, while CPC is used more as an acquisition channel.
Bidding CPM will often get your cheaper clicks and more impressions because FB will be able to calculate how much of your money they'll be able to burn through, while they can't exactly count your dollars when you bid CPC.
Some of my campaigns I start off on CPC just to see what I can get; basically to see the amount of clicks I can get for what I'm bidding. I'll then, and most often, switch over to CPM after I have some figures, and measure those stats against the CPC stats.
Like I said, CPM often gets you more impressions, so if you already know how many clicks you're getting per 1K impressions, then why not bid CPM, when bidding CPM will get your a cheaper CPC at the end of the day.
I hope this helps :/
Disclaimer: I'm not always right, this is just my personal experience and some other marketers will have a different opinion than I.