How precise and stable are you talking? What's the line and load variation (PSRR and output resistance, respectively)? How low is "low noise"? What bandwidth -- it's only going to be a good current source at DC, how much capacitance/inductance/complicated reactance can you tolerate, and at what frequencies?
FWIW, TL431 is in the 70uV RMS noise range (I forget if that's 0.1-10Hz or 10-10kHz or what), which out of 2.5V suggests a noisiness of 0.0028%. You'd of course get worse performance using a traditional current amplifier approach, due to amplifier noise, resistor noise, and environmental limitations (PSRR of the amp itself, bandwidth). There are better references, and there are worse; this typical case would correspond to a "not trying very hard" ballpark of 19.6uA RMS current noise.
BJTs are typically preferred as they have ~10 times the transconductance of a MOSFET (which is, in turn, maybe 10 times the transconductance of its vacuum tube predecessor). Either this gives strong amplification, or low impedances (voltage feedback), or high impedances (current feedback). The intrinsic current mode performance has some limitations (Early effect sets an intrinsic output resistance that can only be improved with feedback; hFE limits collector-to-emitter accuracy, and therefore where you can place the shunt resistor), but it's all around quite handy.
Tim