Nikon D1 has a 3.0MP APS-C (23.7 x 15.5 mm ) sized CCD sensor . On the other hand, Nikon D1X has a 5.0MP APS-C (23.7 x 15.5 mm ) sized CCD sensor .
Below you can see the D1 and D1X sensor size comparison.
Nikon D1 and Nikon D1X have 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 Nikon D1 has 125% larger pixel area compared to Nikon D1X, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.