RAM doesn't make that much difference as long as you have enough of it
Seriously, though... if you have enough RAM that you don't need to rely on virtual memory or significant paging to run apps, then the main difference you'll see IMO is the amount that can remain cached in RAM versus paged out to disk.
While more RAM will mean less waiting to page unused stuff back into RAM when needed again, I think I read somewhere that ultimately Windows likes to page all unused files out to disk whether it has 1.5 GB of free physical RAM or 0.5 GB. In other words, the system with more RAM may be able to hold onto unused files a little longer in the system cache, but wait another 20 minutes and it will be paged out too.
The above statement is really conjecture on my part; I am not sure about this. Can anybody verify one way or another?