To put it another way:
The current in the relay coil is what is holding the contact on the activated position.
When you turn off the drive voltage, any energy stored in the coil (1/2*L*I*I) continues to cause current to flow through the snubber (and the coil).
This energy isn't immediately destroyed, but you do need to get rid of it to cause the current in the coil to fall (to below the contact holding voltage).
If you are using a typical silicon snubber diode with a forward voltage of around 0.8V at the operating current of the coil, your power dissipated in the diode is I*0.8V
When you insert a series zener diode, the power dissipated is I*(0.8+Bvzener), which causes the current to plummet faster (and thus turn off faster).
The tradeoff here, is that now you are dissipating more heat in the zener diode, and also you are presenting a more negative voltage to whatever is driving the relay coil.
There's nothing wrong with using just a regular diode to suppress the back EMF, as long as the relay turnoff time is adequate for your application.