The average user doesn't ever get into the serious Windows memory management problems. Hell, the average Linux user doesn't ever really drive their machine either. But if you do, you'll notice the difference right away. If Windows is rendering something, forget about it doing anything else. Data crunching, same thing. Opening really huge files causes it to flub as well.
Real life experience: I had an Encapsulated PostScript file. It was only about 40MB, but it was 40MB of text, like way over a million lines of code. Using a Windows machine, with 1.5GB RAM and a Pentium4, Adobe Illustrator would not open this file. The amount of memory taken up by Windows combined the amount of memory taken up by Illustrator probably left plenty of room in the memory. But in order for Illustrator to interpret the file, it had to load each and every line separately. Eventually, even 1.5GB RAM fills up, and it starts to swap, but it can't deallocate memory to accomodate moving stuff from RAM to swap. I let it go on like this for over 8 hours before I finally gave up. It just sat there and thrashed the whole time.
So, I put the file on a USBstick and took it home. Loaded it onto my Mac, and attempted to open it in Illustrator. Took about 10 minutes, but it finally came up. And within another 10 minutes, the RAM had been cleared, and I could move around at full speed and get some work done. My Mac has 640MB RAM and a G3 900MHz processor.
Granted, I don't get monster files like this that often. Most people don't. But if you do, you're going to need better memory allocation and deallocation than Windows can provide. Issues that you take for granted, like apps taking forever to minimize/maximize, or thrashing for a few minutes before accepting responses, these things just don't happen in Linux or OSX.