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, Canon 5D MII has a 21.0MP Full frame (36 x 24 mm ) sized CMOS sensor and features Digic 4 processor.
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 moire occurring in certain scenes.
Below you can see the D5500 and 5D MII sensor size comparison.
As seen above, Canon 5D MII has a 2.4x Larger sensor area than Nikon D5500. Larger sensors give photographer more control on the depth of field and blurry background compared to smaller sensor when shot in same focal length and aperture.