Originally Posted by Fan o' water
32 bit os can't write to more than 2 Gb of Ram
... To avoid confusion I should add that this 2GB limit is per application, not the total addressable memory (which is about 3.25). Those are about the only real differences between 32 and 64 bit, there are more little differences but I don't know them.
For downloading, I don't think any downloading application will ever use large amounts of RAM, you can check your Task Manager to be sure.