Nikon D5200 has a 24.0MP APS-C (23.5 x 15.6 mm ) sized CMOS sensor and features Expeed 3 processor. On the other hand, Canon 350D has a 8.0MP APS-C (22.2 x 14.8 mm ) sized CMOS sensor . Nikon D5200's sensor provides 16MP more than Canon 350D'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 D5200 and 350D sensor size comparison.
As seen above, Nikon D5200 has a 1.1x Larger sensor area than Canon 350D. 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.