Check the options of the monitor and turn on scaling. Looks like the settings on the monitor are telling it to run the lower res in it's native size instead of scaling to the full screen.
Although the picture in that case should keep the same quality, just at a lower resolution. For that monitor, I'd upgrade your video card if your power supply can handle it so you can run at the 1920x1080 resolution.
Yeah i was planing on upgrading my graphics card but my main problem is money, not the PSU (my PSU is good. 550W). Maybe i'll upgrade to a Radeon HD 6850 or the GTX 460 (don't even mention the 560 because its way too expensive) XD