here is a simple constant current load circuit from eevblog.com, it's possible that U2 and Q1 might oscillate, a series resistor need to put between U2 and Q1 to stop it.
Some op amps are sensitive to output load capacitance and will oscillate unless there is a resistor added in series with the capacitance. A BJT is much less likely to cause oscillations in that circuit since it has a much lower input capacitance than a MOSFET.