Fujifilm X10 has a 12.0MP 2/3" (8.8 x 6.6 mm ) sized CMOS X-TRANS I sensor and features EXR processor. On the other hand, Panasonic ZS60 has a 18.0MP 1/2.3" (6.17 x 4.55 mm ) sized CMOS sensor and features Venus Engine processor. Panasonic ZS60's sensor provides 6MP more than Fujifilm X10'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 X10 and ZS60 sensor size comparison.
As seen above, Fujifilm X10 has a 2.1x Larger sensor area than Panasonic ZS60. 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.