Is charging an empty Li-Ion cell to 50% more or less efficient than charging it from 50% to 100%?
Obviously this depends on the device itself; but there are quite a lot of Li charging ICs that just dissipate the difference in a MOSFET.

However the graph isn't linear at either end. Take a look at the graphs on http://www.ibt-power.com/Battery_packs/Li_Ion/Lithium_ion_tech.html



The greatest efficiency is in the constant current region, once you get past the initial charge from flat. So in practice you should keep Li batteries between 20% and 80% charge both when charging and discharging, if you want to maximise efficiency and cell life.

Note that the software reporting "state of charge" may lie to you about where "full" and "empty" are - they may already be the 80-20 points.