Are you trying to remove all your information from Facebook, or are you just trying to hide it? That's the question at the heart of your two choices here.
Here's the difference:
-Deactivation means you can log back in whenever you want and everything will return as you left it. Your page will disappear for as long as your account remains deactivated. Friends can't see it, and you'll seemingly disappear from Facebook. BUT! Should you ever choose to return to Facebook, you can simply log back in.
-Deletion means what it sounds like: You're straight up deleting everything you've ever put on Facebook. This does not include messages sent through Facebook Messenger, but does include literally everything else (from your profile information to wall posts). You've got a short window of time between choosing deletion and everything actually being deleted; if you sign in within a few days, you can still cancel the deletion process.
Here's Facebook's official language on deletion: "It may take up to 90 days from the beginning of the deletion process to delete all of the things you've posted, like your photos, status updates or other data stored in backup systems. While we are deleting this information, it is inaccessible to other people using Facebook."