Panasonic LX100 II has a
17.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor and features Venus Engine processor. On the other hand, Olympus E-PM1 has a
12.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor and features TruePic VI processor.
Panasonic LX100 II's sensor provides 5MP more than Olympus E-PM1'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.
Below you can see the LX100 II and E-PM1 sensor size comparison.
Panasonic LX100 II and Olympus E-PM1 have the same sensor sizes so they will provide same level of control over the depth of field when used with same focal length and aperture. On the other hand, since Olympus E-PM1 has 37% larger pixel area (18.45µm2 vs 13.37µm2) compared to Panasonic LX100 II, it has larger pixel area to collect light hence potential to have less noise in low light / High ISO images.