How do I calculate the efficiency of a linear constant current LED driver?
This is a straightforward calculation, since a linear regulator works by acting as a resistor--just the right resistor.  The power it dissipates is the voltage across it times the current through it.  If you put this in series with a 3 volt LED across a 10 volt supply, there will be 7 volts across the regulator.

In fact, since the current through the regulator is the same as the current through the LED, the currents will cancel out in any ratio you calculate, and so you can just use the ratio of the voltages to get your answer.  In this example, 3v/10v or 30% of the total power goes to the LED, while 7/10 or 70% is burned in the regulator.