Nikon D5500 has a
24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Expeed 4 processor. On the other hand, Nikon D1H has a
3.0MP APS-C (23.7 x 15.5 mm ) sized CCD sensor .
Nikon D5500'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.
Another difference between these two cameras is that Nikon D5500'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 D5500 and D1H sensor size comparison.
Nikon D5500 and Nikon D1H 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.