When to use on-click or on-tap w/ Polymer?

Use on-tap all the time, because the semantics of on-tap are better aligned with mobile devices than on-click.

For example, on-click does not fire if another finger is touching the screen, or if the element directly under the finger does not have a mouse handler. There are also some complications with getting on-click to work while you are scrolling. Use on-tap unless there is a compelling reason not to.

You should not use the legacy on-tap anymore since this is deprecated in Polymer 2 and 3. See https://polymer-library.polymer-project.org/3.0/docs/devguide/gesture-events