The GTX 460 is considerably faster than the 6770, it will be able to run most games at maximum at 1920x1080 resolution. The only situations where the 460 would not be better is if you are playing at a very low resolution, or you have a very weak CPU that can't fully utilize all of the 460's power. If you want to run 3 monitors off of a single card, you would have to go with the 6770, as no nvidia cards can run more than 2 monitors off a single card. What resolution are you going to be playing games at? What are the rest of your system specs? It would help to know these things to determine which would be better for you.
Screen size isn't as important as what the display's native resolution is. A 19'' screen could be 1920x1080, or it could be 1680x1050, or even a lower resolution. If your screen resolution is 1920x1080 or 1680x1050, the 460 is the better card. If it is lower than 1680x1050, the 460 may not be much better than the 6770, and it wouldn't make sense to spend the extra money unless you wanted to max out some of the most demanding games out there.