Is there an advantage of one over the other, what are they.
I have a parts Raleigh Olympian that is too big for me with Dia Compe DC500n side pull brakes and considering putting them on my what is looking like my keeper Nishiki with Dia Compe center pulls on it. Is this a good swap, more work for no gain or will I love it?

You won't gain anything in braking or stopping power. You might even find that you have a little less with the sidepulls. One thing to look at consider is most of the older Nishiki's had a fairly long brake length so the side pulls you have may not be long enough exspecially if you want to run 700c wheels at some point.

Thanks, the center pulls stay then.

Yeah. They both work. From a design standpoint, sidepulls don't require a cable hanger. They may have less flex, but total movement of the brake lever is rarely a problem if they are adjusted right. Sidepulls may be a tiny bit lighter, but it's insignificant. Some people argue about which is easier to keep centered, but that's never stuck me as a problem for either one. So unless your current brakes have a problem you shouldn't bother with switching them. The best way to improve braking is to use modern teflon-lined housing with new cables.

Centre-pulls work great, a little harder to set up and adjust with the yoke and straddle cable is all. Just be careful: as the pads wear down, the brake arms have to pivot farther in to make pad contact with the rim. Because the pivots are off centre (unlike a side-pull), the place on the rim where the pads hit will gradually rise until the pads can start to rub the tire instead of just the rim. So you need to slide the pads down a tad as they wear. (The same caution holds for the off-centre arm of a modern dual-pivot brake.) Not a big deal, just something you need to pay attention to.