Well as a matter of geometry, you'll get more screen real estate from a 4:3 ratio screen. The closer you get to square, the more area you'll get from the same diagonal.
You almost HAVE to get a larger monitor if you want a wide screen. Otherwise it would be too short vertically.
Any program that works in Windows is going to work fine on a widescreen monitor, though. The only exception would be a few games (though that's changing). Sure, websites aren't made for wide-screen viewing, but they're not made for huge resolutions, either. So even with a standard resolution monitor, if you have your resolution up and are viewing full screen, the page won't be taking up much of it.
The only time I ever view web pages full screen is on my laptop with it's lower resolutions. On any PC monitor 17" or better, I'm always running at just about the highest resolution it can manage. In that scenario, I view web pages in windows rather than full screen. That's likely what I would do with a widescreen monitor, too. Otherwise, I'd tilt it and view everything vertically.