Low Quiescent LDO vs. Buck Converter: Which is better for low power applications?
as your micro controller is only drawing such a tiny amount of power, an LDO with a low quiescent current, ideally lower than your microcontroller, will likely end up more efficient, most inductor based switching converters struggle at very low loads, 

e.g. the LDO you linked draws 15uA at idle, so your power wasted is 
(the supply current of your micro * The voltage your dropping) + (15uA * the input voltage)

The switching converter has a 1350uA quiescent current, however you can see on the graphs used that the efficiency of the converter falls off to nothing at low currents, so under ideal conditions, you will be burning atleast (9 times the supply current of the micro * the output voltage) + (1350uA * input voltage)

As an alternative there are switched capacitor buck regulators, this would sit fairly close to the LDO for sub 1mA supply currents and a low voltage drop, whether it is better or worse would require knowing exactly how much current you need and how large the voltage drop is. 

edit: deceptive idle current on the switching regulator,