Fujifilm XQ1 has a 12.0MP 2/3" (8.8 x 6.6 mm ) sized CMOS X-TRANS II sensor . On the other hand, Fujifilm XP130 has a 16.0MP 1/2.3" (6.17 x 4.55 mm ) sized BSI-CMOS sensor .
Below you can see the XQ1 and XP130 sensor size comparison.
As seen above, Fujifilm XQ1 has a 2.1x Larger sensor area than Fujifilm XP130. 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.