Different forms of kernel estimation have been used for the construction of spatially continuous earthquake occurrence representations. A method has been developed to quantify the difference between such representations. The method compares seismicity models generated by kernel estimation for an earlier and a later time period to measure the ability of the models to forecast the locations of future earthquakes. Further, the (earlier) models are compared to the distribution of the original earthquake catalog to measure the closeness of representation and data. The method has been applied to historical earthquake catalogs of New Zealand and Australia. We found that kernel estimations with spatially varying bandwidths performed better than kernel estimations with spatially constant bandwidths. The use of a temporal sequence filter improved the match between the earlier and later models. The Gaussian kernel provided better results than the inverse-biquadratic kernel, due to the longer tails of the inverse-biquadratic kernel, which did not describe the distribution of earthquakes in space accurately. A bandwidth of about 1.0 (in area units) for the Gaussian kernel provided the best results, whereas a bandwidth of about 0.4 provided the best results for the inverse-biquadratic kernel.