A 1920x1080 monitor has 2073600 pixels. A 1366x768 monitor has 1049088 pixels, or roughly half as many. That's a MUCH lighter load for the graphics card. If you go from the smaller monitor to the larger one, your FPS could drop by close to half also, although it will also depend on how demanding the game is on your CPU. If it is at all like BF3, expect BF4 multiplayer to depend a lot on the CPU for performance too.
If you're concerned about the larger monitor sapping performance too much, you could: 1) run it at less than its native resolution for games, although that could introduce some fuzziness or unintended blurring, 2) get a 1600x900 (1440000 pixels) or 1680x1050 (1764000 pixels) monitor instead, 3) turn some settings down, or 4) get a more powerful graphics card, like a HD7970 or GTX770 instead.