Asymmetric balls have a Preferred Spin Axis, syms don't.  On a free-spinner like a deTerminator, a ball with a PSA will migrate from the initial spin axis to its preferred axis in a relatively short period of time.  Under 10-11 seconds and the ball has a strong enough PSA to be worth talking about.  Symmetric balls may never find a PSA or may take a long time to do so.

If you want to call them "mass bias" balls, one side of the core has more mass than the other side.  Look at a ball like the Ravage from Morich and you'll see that the core clearly has more on one side than the other.  Other balls, like those with the current Zone cores don't necessarily have more mass on one side than the other.  Cut a Zone in half through the pin and you'll get two halves of equal mass.

The stronger the mass bias, the stronger the asymmetry, the lower the spin time the more influence the MB has on ball reaction.  Asyms tend to be more angular than syms with similar core numbers and covers for a given drilling.  They offer more flexibility layout-wise than syms, and can offer a wider range of reactions based on where the MB is positioned.  But they can also be more sensitive to release, so problems with your release might be magnified by the ball.

SH