How common would water-borne diseases such as Cholera have been in cities that used aqueducts such as Rome? Would the drinking water have been that much safer compared to other cities?

History enthusiast here.

Other cities as in other Roman cities?

To answer your question, considering that the aqueducts were fed by springs quite far away from Rome itself, the possibility of a waterborne illness is quite unlikely. To entertain the possibility would call for some infected body (human, fish, vegetable) to take a dip in an aqueduct (or the spring itself). However, if the source was a stagnant body of water (unlikely as the master planners knew the relation between stagnant water and waterborne diseases), then bid farewell to a large chunk of Rome's population.

To your other question, yes, the aqueduct was vastly superior (in terms of safety) compared to drawing water from a well, spring, or river, as those sources could become easily contaminated over a short period of time.

Sources: http://en.wikipedia.org/wiki/Roman_aqueduct

http://www.romanaqueducts.info/picturedictionary/pd_onderwerpen/hygieneandhealth.htm