How to select which iOS device receives push notifications (for Facebook)
Just of note that Facebook is notorious for being extremely flakey when delivering notifications of any kind (whether they be system wide through the home screen icon, or even in-app). If you have Push enabled on both devices, the problems could lie within Facebook.

Also note that it may (read: should) be the case that when you check your account on one device, the notifications should disappear on the other, as they will be marked as read.

Additionally, it could be that Facebook's servers deliver a notification only once to any waiting device capable of handling them (remember they have millions of users to contend with). You'll have to contact Facebook to make certain of this however.

You can use mail to test it. If you send yourself an email, do you receive notifications on both devices? If you read the mail, do they disappear (get marked as read) on both devices?