Fujifilm XQ2 has a 12.0MP 2/3" (8.8 x 6.6 mm ) sized CMOS X-TRANS II sensor and features EXR Processor II processor. On the other hand, Olympus E-PM2 has a 16.0MP Four Thirds (17.3 x 13 mm ) sized CMOS sensor .
Below you can see the XQ2 and E-PM2 sensor size comparison.
As seen above, Olympus E-PM2 has a 3.9x Larger sensor area than Fujifilm XQ2. 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.