Canon 1Ds MIII has a 21.0MP Full frame (36 x 24 mm ) sized CMOS sensor . On the other hand, Canon 5D MIV has a 30.0MP Full frame (36 x 24 mm ) sized CMOS sensor and features Digic 6+ processor.
Canon 5D MIV's sensor provides 9MP more than Canon 1Ds MIII'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 1Ds MIII and 5D MIV sensor size comparison.
Canon 1Ds MIII and Canon 5D MIV 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 Canon 1Ds MIII has 43% larger pixel area compared to Canon 5D MIV, it has potential to collect more light on pixel level hence have less noise in low light / High ISO images.
DxOMark Sensor Scores
DxOMark is a benchmark that scientifically assesses image quality of camera sensors. It scores camera sensors for color depth (DXO Portrait), dynamic range (DXO Landscape) and low-light sensitivity (DXO Sports), and also gives them an overall score. Canon 1Ds MIII and Canon 5D MIV sensors have been tested by DxO and the results show that 5D MIV has a better overall score of 91, 11 points higher compared to 1Ds MIII's score of 80.