If you take the example of the BZX79C5V1 zener and read the data sheet it tells you that a 5V1 zener diode produces nominally 5.1 volts at 5mA of current flowing thru it. If you read a bit deeper, there is a "differential resistance" associated with the zener and for a 5V1 zener at 5mA this is nominally 40 ohms.
This basically means that the 5mA causes a volt drop 0.2 volts across this resistance and the rest of the volt drop (4.9 volts) can be modeled by a perfect zener at 4.9 volts. This tells you that if the current through the zener was increased to (say) 5.1 mA, the terminal zener voltage will change to 5.1mA*40 + 4.9 volts = 5.104 volts.
This is far worse than a moderately priced voltage reference chip because the voltage ref will ensure that the current into its "internal reference" is held constant across a wide range of supply voltages.
Most zener diode specifications do not contain details of how the zener diode terminal voltage changes with operating current (so you are a bit in the dark) but it's noteworthy that the differential resistance gets bigger for smaller zener currents and if you are loading the zener with a potential divider any expectations of an accurate voltage will be diminished.
Having said all of that, if your power supply is a little unstable in voltage then a zener diode ref will be better than a potential divider taken directly from the rail (unless you are using an ADC and taking ratiometric measurements using the supply as voltage reference).