If you are looking to find out which way the user sees the interface then use the interface orientation. I suppose both methods are fine.
If you want to find out which way the physical device is positioned use the device orientation.
Note that interface orientation is different from the device orientation (so there is no such thing as "interface orientation of device").
Device orientation can be flat up/flat down (Interface can only be portrait/upside down/landscape right/left). Device orientation might also be different if the device is rotated but the interface is set to a constant one. Plus landscape orientations are reversed e.g. device landsapeRight == interface landscapeLeft.
I am not sure when face up/down might be useful.
Just in case you need the actual methods, you can check the interface orientation from a view controller using this:
UIInterfaceOrientation orientation = self.interfaceOrientation;
Or from any class in the app using this (status bar check):
UIInterfaceOrientation orientation = [[UIApplication sharedApplication] statusBarOrientation];
Get the device orientation like this:
UIDeviceOrientation orientation = [[UIDevice currentDevice] orientation];