The black corrugated culverts you refer to are probably HDPE not PVC.
In a nutshell:
HDPE
Pro: usually less expensive. Because it is lighter, it is easier to install in most situations.(wants to float in a wet installation)
Con: much less forgiving than RCP when installed improperly. poor practices in bedding and backfill leads to dramatic failures. (poor construction practices can still lead to RCP problems esp. joint failure)
RCP
Pro: contractors are used to working with it...more familiar. more forgiving than HDPE for bad installation practices. Depending on class of pipe, can be used in shallower cover situations.
Con: typically more expensive material and installation.