Cement board has a higher density than 5/8 drywall. It also probably, and this is just a guess, probably has a lower resonance as well (being cement), so less sound should get through.
5/8" drywall is about 2.2lb per sqft.
1/2" cement board is 2.355 lbs per sqft.
The price is comparable between the two, with cement board being a little more expensive but not by much. 1/2" cement board comes in 3' x 5' sheets, at about $10 each (about 67 cents per sqft). 5/8" drywall comes in 4' x 8' sheets at about $15 each (about 47 cents per sqft).
Is 1/2" cement board a better soundproofing material than 5/8" drywall?