Leica D-Lux Typ 109 has a
13.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor . On the other hand, Olympus E-M1 III has a
20.0MP Four Thirds (17.4 x 13 mm ) sized CMOS sensor and features TruePic IX processor.
Olympus E-M1 III's sensor provides 7MP more than Leica D-Lux Typ 109's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
One other difference between these two cameras that is worth mentioning is that Olympus E-M1 III's sensor doesn't have an anti-alias (Low-Pass) filter. Removing anti-alias filter increases the sharpness and level of detail but at the same time, it increases the chance of moiré occurring in certain scenes.
Below you can see the D-Lux Typ 109 and E-M1 III sensor size comparison.
Sensor Size and Resolution Comparison image of Leica D-Lux Typ 109 and Olympus E-M1 III Cameras
Leica D-Lux Typ 109 and Olympus E-M1 III have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.
Sensor size sets the circle of confusion, so it drives how much depth of field each
of these bodies gives you at a given aperture. You can calculate it exactly for the
Leica D-Lux Typ 109
or the
Olympus E-M1 III ,
including hyperfocal distance.