The Dell UltraSharp U2412M has a response time of 8ms. A good gaming monitor should have 2ms or less to avoid ghosting. While 1920x1200 is a slightly higher resolution, if you are gaming the Viewsonic will be much better.
There's nothing wrong with Viewsonic, I've used them in the past and they make great monitors. However, I just looked up the 27" 1ms Viewsonic the OP was talking about and it has no DVI input. If you are using HDMI then this isn't a problem, but just something to be aware of.
The Dell is an IPS-LCD monitor. IPS monitors provide a much better viewing experience by offering more accurate color/contrast, and better viewing angles. These monitors are designed for graphic designers and professional photographers.
The Viewsonic is a TFT-LCD monitor, which are much cheaper and have faster response times than IPS-LCDs. The monitor you own now is likely an TFT-LCD.
Most gamers prefer TFT displays because they value faster response times more than they value image quality.
However, I argue that most gamers have never played on an IPS display before. If they had, they might not be so quick to dismiss a beautiful looking display (the Dell U2412M) in favor of a s*!t display with a 2ms response time. Furthermore, the response time on new IPS monitors pretty good, and should be good enough for most gamers.
Unless you are a professional FPS gamer, go with the Dell U2412M or U2410. Once you go IPS you can't go back