Not to mention, under what transients, surge conditions, and statistics thereof? Operating temperature range, and statistics thereof?
Given perfectly smooth DC, and purely electrical means of testing, I suspect the answer to both is "longer than you can tell".
The LED has a failure mechanism due to charge trapping, causing reduced emission efficiency with use, and white LEDs the phosphor gets "bleached" so to speak. But these don't have consequences as measured at the terminals; maybe the V(I) curve shifts some, but I'm not aware of any mechanism by which it shifts outside of nominal ratings.
We use LEDs for their emissions, obviously, so typical ratings are based on that.
I would expect the LED to have a shorter life.
The LED is direct polarized, Zener is reversed polarized, so the E field for the same voltage would be stronger inside the LED junction. I would expect a stronger electric field to eventually pull atoms from their place and mess with the crystalline structure of the junction.
Another argument might be the energy level jumps of the electrons. To emit visible light the difference in energy levels are higher, so more wiggle that, combined to the thermal wiggling, might eventually irreversibly damage the junction.
These are just cherry picked arguments based on qualitative guesses. Didn't make any estimation, and I have no idea if these will stand true in a quantitative evaluation.
Strange, I would pick the zener: its junction is extremely thin (tunneling is occurring), and the bandgap, and binding energy, is lower for Si than AlGaAsP. (Or at least, most alloys, probably.) (Well, binding energy, or even just atomic dislocation energy, I'm not too sure of? I *think* bandgap must be strictly less than binding energy, otherwise electrons alone could rip the stuff apart -- but dislocation, I don't know about. Funny thought...)
Tim