How is the Zener inefficient? Will it allow 2.7v to pass into the cap even when it produces voltages in excess of 2.7v? I'm really confused as to how a Zener works.
If the voltage is above 2.7v, then yes, from the top of the (2.7v) zener to the bottom (call it ground), is 2.7v (give or take, tolerances etc etc).
But the extra volts don't just vanish, the power has to go somewhere.... heat.
Let us imagine that your load is going to be fed 100mA, and that your panel is producing that at 6v.
The resistor must by definition drop 6-2.7 = 3.3v, if 100mA is passing through that resistor, then how much power is being burned off as heat: 3.3*.1 = 330mW of power, that's a lot of power loss. Gets worse, because the zener also must pass current through it, lets say 5mA, so your resistor passes 105mA (100 to the load, 5 to the zener), increasing the power dissipation further.
All that power is thrown away, which for solar applications, is generally the opposite of what you want :-)
You also have the problem that if your load stops being a load, that is the amount of current it is drawing drops, because you have a fixed resistor, all that current it was using must by definition now go through your zener, which in the best case get's hotter (now the zener has to dissipate .105*2.7 Watts of power), or in the worst case goes pop.
Zener based regulation (and linear regulators in general for that matter) is fine if you don't care much about chucking out useful power, and if the load is fairly constant.