Fujifilm XQ1 has a 12.0MP 2/3" (8.8 x 6.6 mm ) sized CMOS X-TRANS II sensor . On the other hand, Canon SX610 HS has a 20.0MP 1/2.3" (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features DIGIC 4+ processor. Canon SX610 HS's sensor provides 8MP more than Fujifilm XQ1'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 XQ1 and SX610 HS sensor size comparison.
As seen above, Fujifilm XQ1 has a 2.1x Larger sensor area than Canon SX610 HS. 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.