Nikon D1H has a
3.0MP APS-C (23.7 x 15.5 mm ) sized CCD sensor . On the other hand, Sony A77 has a
24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Bionz processor.
Sony A77's sensor provides 21MP more than Nikon D1H'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 D1H and A77 sensor size comparison.
Sensor Size and Resolution Comparison image of Nikon D1H and Sony A77 Cameras
Nikon D1H and Sony A77 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
Nikon D1H
or the
Sony A77 ,
including hyperfocal distance.