Sony RX100 II has a 20.0MP 1" (13.2 x 8.8 mm ) sized CMOS sensor . On the other hand, Fujifilm XP200 has a 16.0MP 1/2.3" (6.17 x 4.55 mm ) sized CMOS sensor .
Below you can see the RX100 II and XP200 sensor size comparison.
As seen above, Sony RX100 II has a 4.1x Larger sensor area than Fujifilm XP200. 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.