Some people report that 64-bit Ubuntu is a little faster, but that might be a subjective thing, depending on what programs you use. I found that the 64-bit version was possibly a little faster on mine (also 4GB of RAM and an Intel dual core CPU), but I never actually timed things so I can't really say for certain, although it did feel faster. It's been extremely stable for me, too, but if the 32-bit has been stable for you, then that might not be relevant.
However, your system has the hardware for the 64-bit Ubuntu, and there don't appear to be any limitations (such as programs that won't run on it), so give it a shot. Of course, you can always install it next to what you have and compare, which would allow you to get your own feel for how it works.