Generally speaking, the more pixels the larger the viewing area, but it depends on how the game is designed to handle the different aspect ratio.
For example, in StarCraft 2 if you play in 1920x1200 resolution the overhead view looks a little more zoomed in when you compare it to 1920x1080 resolution which gives the game a more zoomed out look so that you can see more of the map. For cases like this having a 1920x1200 resolution monitor means you can also change the resolution to 1920x1080 to see if that aspect ratio significantly changes the view of the game.
I think some console port to PC games only support 16:9 aspect ratio resolutions (like 1920x1080 and 2560x1440) so on a 1920x1200 resolution monitor there will be black bars on top and bottom.
Lastly since 1920x1080 resolution is lower than 1920x1200 resolution, you will get slightly better performance because the graphic card has less pixels to push.
Outside of games, I find it easier to multitask and surf the net on a 1920x1200 resolution monitor and I would personally choose a 1920x1200 resolution monitor over a 1920x1080 monitor any day of the week. I have a 1920x1080 monitor (Asus VK246H) and I don't really like it. I'm going to replace it with a 1920x1200 either at the end of this year or early next year.