The best buck may be the best choice:
The very best available buck converters will be superior to a linear regulator.
Consider the battery range to be 4.0V down to 3.4V (ignores initial brief period above 4.0V and allows 0.1 V output headroom).
Vin = 3.4 min, 3.7 mean, 4.0 max.
For 3.3V out a linear regulator gives efficiencies of
3.3/3.4 = 97%, 3.3/3.7 = 89% and 3.3/4.0 = 83%
Actual mean efficiency will depend on cell used and load level etc but say 3.7 Volt in is typical (which it probably is) for 89% efficiency.
A very good buck regulator with synchronous switching and careful attention to detail should be able to reach around 95% for much of this range. The difference between the linear and buck supplies is small, but notable.
Ground current can be a VERY bad performance measure:
Note that using ground current as a figure of merit for a linear regulator can be VERY misleading. eg imagine a linear regulator with zero ground current and Vin = 3.6V and load = 1 mA. The efficiency will be 3.3/3.6 = 91.7% so about 8% of the input energy will be lost. This is equivalent to a regulator with 100% conversion efficiency but a ground current of 8% of the load. ie here 8% x 1 mA = 80 uA. So even if the regulator has 10 uA ground current at 1 mA load this will be swamped by unavoidable conversion losses across most of the Vin range,
Finding an IC to meet the above spec will take care. Buck regulators usually give peak conversion efficincies for limited combinations of Vin Vout, load and more. Outside optimum ranges the efficiency will fall off - sometimes badly.
I looked at the Digikey parametric selection guide to see if a suitable part could easily be identified. It's not an instant task as eg setting Iout_max to 100 mA may mislead as the most efficient IC may have a switch capable of switching higher current than is needed.