Forget symmetric/asymmetric. A better term in the case is mass bias. The ball has a mass bias. Other cores like, say, some of the Morpheus core and the old Morich Ravage core, clearly have more mass on one side than the other. There simply isn't mass on the other side. The Centrex core has more mass on one side than the other and they use different density materials to do it. The RAD core from Storm is the same way. Storm shows you which pieces have different densities by coloring the discs differently on the website. Ebonite doesn't.
Asymmetric, mass bias, whatever. Both mean the ball has a preferred spin axis. And PSA is, to my mind, a much better term. Some balls, like the Zones, it's not obvious which side of the ball is heavier than the other, there's no clear mass bias. Likewise with the Vanguard core. Without weighing it, there's just no way to say "there's more stuff over here on this side".
But we measure the strength of that asymmetry, that mass bias, by putting it on a deTerminator and measuring how long it takes to reach its preferred spin axis. We also measure the RGs on three axes and that also provides a differential to indicate strength, but three-axis RG values aren't always given.
SH