Both Panasonic ZS1 and Kodak Mini have 10.0 MP resolution sensors but Panasonic ZS1's sensor is 1/2.5-inch (5.744 x 4.308 mm ) and Kodak Mini's sensor is 1/3-inch (4.8 x 3.6 mm ).
Since Panasonic ZS1's has a larger sensor area with the same resolution, this means that it also has a larger pixel area hence better light collecting capacity for a given aperture compared to Kodak Mini.
Below you can see the ZS1 and Mini sensor size comparison.
As seen above, Panasonic ZS1 has a 1.4x 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.