`As a note, some codes specify you use only PVC or ABS (almost all allow metal). Also because of codes, sometimes there is a stronger availability of one type of plastic or the other, again, so you may want to choose the more common ("regional availability"). One type may be cheaper in your area, as well, another factor. For larger buildings you may be required by code to use metal.
PVC (at least sched. 40 thickness is required):
Lasts "about forever," resists corrosion, cheap. Doesn't sag as much as ABS (on very long horizontal pipes, for instance). Requires both a primer and glue, which is more work to install). Fittings may hold up better. Typically white. Is said to be slightly quieter than ABS. If on rooftop (i.e. vent) might degrade more quickly than ABS. It's rumored to be more brittle than ABS in cold climates (shatter more easily), though typically your sink drain pipes might be exposed to temperature extremes (vents on the roof might though). Temperature rating is max 180 °F (typically high enough for typical drain use). Might be more resistant to chemicals, if it's a laboratory. Might shatter more easily after being exposed to cold a lot.
Lasts "about forever," resists corrosion, cheap. Can glue without a primer (faster install/labor). Typically black. Apparently it can deform if left in the sun for short periods of time, though PVC and ABS both become brittle if left in the sun for long, so be careful there, possibly painting vents, etc. Is said to have better impact strength (read "smash it with a hammer") than PVC, though hopefully you're not accidentally smashing pipes anyway. It is said to "continue burning" after the flame is extinguished, therefore sometimes disallowed in commercial buildings. Is said to have worse fittings over time than ABS. Temperature rating -40 °F to 180 °F.
In the end, ABS is "made for" DWV, and works great. PVC also works great. Note that you cannot trivially direct connect (as in glue) ABS to PVC pipes, some codes require a special joining connector, etc. This isn't as big of a deal with sink drains (since you're screwing it into the wall anyway, not gluing it together) but is for normal pipe lines. It may be worth it to "stick with what's already there" (ex: what's in the wall) in case it adds stability. Some people seem to prefer ABS, some PVC. Since the drain is indoors, so few temperature extremes, no long pipes, they'll probably both work under the sink.
More fire safe. Less noisy (frequently used for vertical pipes because of that). Can gets lime deposit build-up, etc over time, especially on smaller pipes. You can chrome plate it for looks.
More fire safe. Susceptible to chemicals poured down it and corrosion over time causing it to weaken. You can chrome plate it for looks.