Does it matter what kind of pipe is used for a sink drain?
There are two main factors that determine what is used:


Code requirements (as well as the project's specifications)
Cost


ABS and PVC are the cheapest, however there can be limitations with their use in larger buildings due to fire code requirements.

Where fire codes requirements limit the use of plastics, either cast-iron or DWV copper is used for the piping above ground switching to either Chrome or Brass p-traps for the sinks. However depending on the authority having jurisdiction (usually the local inspector), PVC or ABS p-traps may be permitted within the sink cabinet.

XFR-PVC is a kind of fire resistant PVC, and does meet flame and smoke spread requirements and, depending on the project, may be allowed to be used instead of Cast-iron or DWV copper where metal is typically required.

Chrome plated metal is also used for wall hung sinks where the p-trap will be left exposed.

Labs that use chemicals and acids typically use either glass or special acid resistant plastic pipe and p-traps.