Hi,
The quick answer is "yes"; however you need to TWEAK all the settings and that includes the resolution. You should NOT be running at 1920x1080.
This issue has been in the news lately with the XB1 vs PS4 video that shows the XB1 running 720p upscaled. There's a REASON for that. The game looks better at 720p (upscaled) then it would at 1080p which would then sacrifice quality in other ways.
You're also going to have to aim for a specific target frame rate. If screen tearing isn't too bad, I suggest VSYNC OFF and 40FPS average (monitor with FRAPS). If tearing is too bad, you'll have to aim for VSYNC at 30FPS or 60FPS. Unfortunately, 60FPS is likely not attainable and 30FPS with VSYNC would feel sluggish. That's the choices though when playing a demanding game.
Example:
1) Start FRAPS/BF4
2) choose 1600x900 or 1366x768
3) tweak Shadows, anti-aliasing etc to find the best balance that meets 40FPS
4) repeat later in game if gets more demanding.
Finding the best settings takes practice.