There's a lot of confusion about what a bigger monitor, or a different aspect ratio, actually means when it comes to playing games.
The short answer is that, if the resolutions are the same, but the monitors differ in size, what you see is identical in terms of coverage; the only difference is that the smaller monitor will have a lower dot pitch (smaller pixels, more densely packed together) which makes it look a little better. In practice, the difference is barely noticeable. People tend to prefer the larger screen regardless (e.g. 22" TFTs are now preferred to 20" TFTs with the same resolution).
It's a common myth that, if you change from an x inch 4:3 monitor to the same sized (in inches) widescreen, you see 'more', as if the wide aspect ratio only extends the screen. In fact, you actually see
less. Surface area of a monitor varies with the aspect ratio; different aspect ratios offer different surface area sizes. As the aspect ratio tends towards 1 (i.e. a square screen), you get the maximum surface area.
As a result, if you get a 16:10 monitor, the surface area is actually slightly smaller than the equivalent 4:3 monitor.
For example:
* 20" widescreen has 1680x1050 pixels = 1,764,000 pixels in total.
* 20" normal aspect has 1600 x 1200 pxiels = 1,920,000 pixels in total.
I.e. the normal aspect 20" has approximately 9% more pixels -- is it any wonder that manufacturers are happy with the rise of widescreen?

. Now who's seeing more ingame? It certainly isn't the widescreen user. (If you don't believe me: have a look
here)
The flipside of this is that widescreens are more natural -- human vision is widescreen. I can hold my hands out in the 'da vinci' pose and waggle 'em around and still see them using peripheral vision. I certainly can't do the same thing vertically. The argument would probably be that the widescreen view, while smaller, has a shape that is more useful for gaming because you're more likely to be scanning the screen horizontally than vertically. I personally think that widescreen really starts to make sense at 22" and above. I'm sitting behind a 4:3 aspect 20" TFT and if it extended up any further, I'd have to crane my neck a bit to see it. If I buy a 24" widescreen, it's basically exactly the same height, but extends left and right -- it makes sense.
A further myth is that a larger resolution using the same aspect ratio results in seeing more. Games have a field of view calculation and it uses the aspect ratio -- nothing more, nothing less. The aspect ratio does not vary as long as different monitors have the same ratio of length to height.
End result is this:
Someone playing at 800x600 on a 15" monitor = aspect ratio of 800/600 = 1.3333 (4:3)
Someone playing at 1600x1200 on a 20" monitor = aspect ratio of 1600/1200 = 1.3333 (4:3)
The 1.333 is what's put into the calculations to set up the player's field of view. We're only interested in the ratio between horizontal and vertical pixels, not the pixels themselves.
The only difference is the clarity of what you're seeing; the player with the 20" monitor will maybe see 4 pixels of an enemy's head in the distance, whereas the player with the tiny 15" monitor will either see a single pixel, or maybe not see it at all.
I personally run a 20" 1600x1200 TFT. I also use a 19" 1280x1024 TFT at work. I game on both and the difference is very small (in fact, the 19" has better responsiveness and colours, so I prefer it). I haven't used a 22" so I can't personally say whether it's worth upgrading to one.
Going to a 24" (assuming your graphics card can hack it) would most likely result in a warm tingly feeling, though. That's what I plan to do soon (as soon as I figure out which non-TN film 24" has the least input lag).