LDO vs. Step-Down DCDC using LiPo
Reducing a 4.2V source to 3.3V with the linear regulator represents an efficiency of about 3.3V / 4.2V ≈ 78.57% regardless of current. The efficiency increases as the source voltage decreases, up to 3.3V / 3.4V ≈ 97.06% (assuming a 100mV dropout worst case), with a small drop to 3.2V / 3.3V ≈ 96.97% before the cutoff is reached.

The switching regulator has an efficiency of about... we'll call it 90% at the currents you are considering. The linear regulator will only reach 90% efficiency with a source voltage of 3.3V / 0.9 ≈ 3.67V, which the battery will reach with about 35-45% of its energy left.

It is also possible that the final switching regulator design will have less efficiency than given in the datasheet, in which case the linear regulator is at even more of an advantage. And of course below about 80% it would be silly to use the switching regulator at all.

So the switching regulator will probably last longer on the same amount of battery assuming a high enough efficiency, but requires additional passives compared to a linear regulator and is noisier due to the pass element turning on and off. The linear regulator has a simpler design with less noise, but will likely burn through the battery a bit faster.