Olympus E-P7 has a
20.0MP Four Thirds (17.4 x 13 mm ) sized CMOS sensor and features TruePic VIII processor. On the other hand, Olympus E-P1 has a
12.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor and features TruePic V processor.
Olympus E-P7's sensor provides 8MP more than Olympus E-P1'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.
Another difference between these two cameras is that Olympus E-P7's sensor lacks 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 E-P7 and E-P1 sensor size comparison.
Olympus E-P7 and Olympus E-P1 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.