Nikon D5300 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 60D has a 18.0MP APS-C (22.3 x 14.9 mm ) sized CMOS sensor and features Digic 4 processor.
Nikon D5300's sensor provides 6MP more than Canon 60D'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.
Another difference between these two cameras is that Nikon D5300'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 D5300 and 60D sensor size comparison.
As seen above, Nikon D5300 has a 1.1x Larger sensor area than Canon 60D. 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.
DxOMark Sensor Scores
Both Nikon D5300 and Canon 60D sensors have been tested by DxoMark. DxoMark 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. Of the two cameras that we are comparing, D5300 has scored 83, 17 points higher than 60D.