Supersample can look great and was the standard AA for years, but it can not make up for a lack of pixels.
Now on paper this sounds like, get another screen, but it may not be the case.
Are you happy with your current setup?
How large is the screen?
Pixel density is one of those things that can make one screen look better than another(larger screens tend to have higher resolution). So a 1920 x 1080 32 inch screen will have larger pixels than a screen of the same resolution at 22 inches. These larger pixels may show edge jaggies more so screen size and your distance from the screen plays a role.
This pixel density can also work against you in some cases. If you have a screen that has a resolution of 1920 x 1080 and is 15 inch, things may look to small(but this is the direction we are heading in because the ppi/megapixel war of phones/tablets is spilling over to the computer side.). The all come down to personal preference and most operating systems can do some scaling(Windows is not quite at the top of its game in this department because it has lots of backwards compatibility.)
Are you waiting to see how 4k pans out? If so, it may be worth hanging onto what you have now.
You do gain some desktop space with a higher resolution screen as well. I do not find the internet is exactly ready for higher resolution screens yet as most websites still have empty space on the sides(or evenly placed to pad the site) even at only 1366 wide. This site has almost 500 pixels of space on the sides(of the content) on a 1920 x 1080 screen.
I am going to call personal preference on your display. You can not make extra pixels, but games can still look pretty good.