Kodak Mini has a 10.0MP 1/3-inch (4.8 x 3.6 mm ) sized CCD sensor . On the other hand, Sony TX200V has a 18.0MP 1/2.3-inch (6.17 x 4.55 mm ) sized BSI-CMOS sensor and features BIONZ processor.
Sony TX200V's sensor provides 8MP more than Kodak Mini's sensor, which gives a significant advantage in real life. You can print your images larger or crop more freely.
On the other hand, please keep in mind that Max sensor resolution is not the only determinant of resolving power. Factors such as the optical elements, low pass filter, pixel size and sensor technology also affects the final resolution of the captured image.
Below you can see the Mini and TX200V sensor size comparison.
As seen above, Sony TX200V has a 1.6x Larger sensor area than Kodak Mini. 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.