voltage source vs. current source
There are no advantages or disadvantages.  Some devices require constant voltage.  Some devices require constant current.

Majority of the DUTs** require constant voltage.  That's why most of the bench top power supplies, which you have encountered in the labs, are constant voltage.  Keep in mind that a descent lab power supplies have and adjustable max current threshold and 2 modes: constant voltage (CV) and constant current (CC).  CC mode is activated automatically, when the DUT tries to pull more than the max current.  Often, it's a sign of a problem, when a DUT wants to pull more current than expected.

Few DUTs require constant current.  LEDs, for example.  Often, a constant voltage supply powers a separate constant current circuit, which in turn powers a constant current DUT.

** DUT - device under test