Canon 1D has a
4.0MP APS-H (28.7 x 19.1 mm ) sized CCD sensor . On the other hand, Canon 1D MIII has a
10.0MP APS-H (28.7 x 18.7 mm ) sized CMOS sensor .
Canon 1D MIII's sensor provides 6MP more than Canon 1D'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 1D and 1D MIII sensor size comparison.
Canon 1D and Canon 1D MIII 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.