Canon SX240 HS has a
12.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features Digic 5 processor. On the other hand, Fujifilm F800EXR has a
16.0MP 1/2-inch (6.4 x 4.8 mm ) sized EXRCMOS sensor and features EXR processor.
Below you can see the SX240 HS and F800EXR sensor size comparison.
Canon SX240 HS and Fujifilm F800EXR have almost the same sensor size, so neither of them has any significant advantage over the other in terms of providing control over depth of field when used with the same focal length and aperture.