Nikon D3 has a 12.0MP Full frame (36 x 23.9 mm ) sized CMOS sensor and features Expeed processor. On the other hand, Nikon D4 has a 16.0MP Full frame (36 x 23.9 mm ) sized CMOS sensor and features Expeed 3 processor.
Below you can see the D3 and D4 sensor size comparison.
Nikon D3 and Nikon D4 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 D3 has 34% larger pixel area compared to Nikon D4, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.