Hi Mark,
This is normal. For any given data set, the improvement in resolution always comes from a SNR reduction with drizzle. Drizzle performs a convolution with a more peaked, smaller PSF, when you use a Gaussian drop kernel. In SNR terms, the effect is similar to lowering the drop shrinking parameter: drops are smaller and hence transport less Bourbon, so the final integrated image is less happy
Since Gaussian and variable shape kernels already reduce the volume of each drizzle drop, you should set drop shrinking to 1 when you use them, unless you have a really huge data set. Whether using these kernels to achieve a resolution improvement is worth the associated SNR reduction is up to you, and depends on the data you have, on what you want to get, or what is more interesting for you. Experiment.
