As Stormy said, Most games are 32 bit apps, and can not/will not use more than 2GB of RAM.
Overall, for what your doing you won't notice any real improvement.
Certain applications and tasks do take advantage of all that extra RAM, making it worthwhile though.
Only if you do a lot of Heavy Photoshop work, HD Video Encoding, and multiple Virtual machines for example, will that extra RAM truly have any benefit.
Otherwise, the only benefit you really gain is Windows allowing a larger footprint.
Meaning, allowing more items to staty in memory, and Pre-Fetch/Super-Fetch will Pre-load lots more.
There is a benefit in this regard, and ALT+Tab seem slightly smoother.
BUT, its hardly worth the extra cost of the additional RAM IMHO, if you do not do any of the things such as I listed above.
The performance gain is so small, most would never even notice it.
I seldom exceed the 4GB mark when doing typical, daily things. Even gaming.
For example, My machine with 8GB, normally idles @ around 2 - 2.4GB use.
However, when gaming, even with multiple apps running in the background, it seldom goes over 4GB.
I have to try hard to get it too.
Now, editing 1080P video with multiple scripts open ... Thats a different story entirely as it does make use of it.