If it's limited at 1680x1050, then that's your problem. Your monitor is displaying 1920x1080 but the picture it's displaying is only 1680x1050, so you end up with around three hundred thousand pixels that aren't doing anything. Hence, letterboxing.
Try going through the control panel in windows and seeing if it can force it up to 1080p.
In the control panel, it says 1920 x 1080 (Recommended, 3D), and in the Catalyst Control, it is set to 1080p. but even with those settings, i'm still getting the letterbox
i5-4670K / 8GB Vengence / Radeon HD 7950 3GB 384-bit GDDR5 (6877 MB total available graphics memory) / Samsung 120GB / Seagate Barracuda 1T / Windows 8