Fujifilm XQ1 has a 12.0MP 2/3" (8.8 x 6.6 mm ) sized CMOS X-TRANS II sensor . On the other hand, Panasonic ZS1 has a 10.0MP 1/2.5" (5.744 x 4.308 mm ) sized CCD sensor .
Below you can see the XQ1 and ZS1 sensor size comparison.
As seen above, Fujifilm XQ1 has a 2.3x Larger sensor area than Panasonic ZS1. 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.