It's definitely easier to follow a higher click resolution for medium and low tempo songs. It's also easier to follow a drum pattern, since it feels like playing with another drummer.
But the most important part of playing with a click is to be able to hear it! A musical mix is nice, but when it comes to playing with a click, it should be perhaps the loudest thing in the drummer's mix. That doesn't mean the mix becomes louder, it means lowering/eliminating any sounds that might clutter the mix and your ability to clearly hear the click.
When a click is introduced into a performance (or recording), the drummer's role changes. It's no longer so much about playing with the band, as it is about playing with the click. It's a bit of a perspective shift, and it's important that drummers grasp that in order to remain viable for most popular music.
In concert, about 2/3 of our show is on a click and linked to video and pre-recorded audio parts, and any 'movement' on my part would be obvious and disruptive. Because I have a very specific click-heavy mix - probably unlistenable to anyone else - I can stick with it like glue. I've never, ever lost the click, and occasional inevitable straying/flamming is within 1/16 note and audible only to me. I'm not some amazing timekeeper, I'm just saying that I treat the click as the most important element of the songs in question, and that allows me to stay on it without fail.