Hi,
As precise as general active op-amp current limiter circuits, not like only BJT with a sensing resistor to make the 500-700mV bias voltage !
If an engineer asks for precision ... he usually expects values with units.
I don't know which Opamp you refer to, and which circuit you refer to.
For sure there are Opamp circuits to generate accurate (indeed I think you ask for accuracy rather than precision) current with less than 0.01% error, most of them maybe are within 2% error, but still there are a lot with more than 10% error.
Indeed almost any voltage regulator or adjustable voltage reference can be (mis-)used as current limiter.
You need at least a shunt and a Mosfet.
But the question is: can it fulfill your requirements on reaction time .. which may cause overshoot (time, value)
When your regulation system is out of regulation (too low input voltage, too high load resistance...) the output saturates (and maybe the input stage, too). There are (old) Opams, they need several 10s of milliseconds to come out of saturation.
******
Accuracy: = absolute accuracy. Accuracy error = deviation from the expected value. Let's say you expect 100mA but the circuit generates 98mA, then there is a 2mA or 2% accuracy error.
Precision: = repeatability. Let's say your circuit produces currents in the range of 97.7mA to 98.3mA with different situations like different temperature, different load resistance, different time .... then the precision error is +/-0.3mA or +/-0.3% (although the accuracy error is 2%)
Klaus