I use the brick path in """developed""" areas, so like the neighborhoods and other areas around my town hall and my shopping district. These paths I usually have pretty wide and use fruit or hardwood trees around them. I use the stone path for the "woodsier" areas like the neighboorhoods i have up on a different elevation with more of the cedar trees and they're a little bit skinnier roads to preserve a lot more greenery.
When I'm not using custom paths, I use the stone paths, though they look less like paths, and more like random stone patches. (Meant grass has overgrown them.)
My main path is stone since my island theme is a forest town. It's very versatile and natural looking. I like to use some of the other paths for accenting in certain spots though. For example, I have some arched tile stones in my small fairy garden and I used the wooden path for a loft type of area on my cliffs with log furniture embellishing it.
I like using the stone one, but not as a whole path. I like having spots just here and there, as if there used to be stone and the grass is taking back over.
Me personally, I use the brick and dark wood path a lot.
My island is pretty basic for that reason though I try to mix it up a bit with path patterns and shapes.
I use the dirt path as my main path, with the dark dirt path as my secondary. I do have a park area near my RS for which I've used the cobblestone to draw a flower pattern under the fountain, but for everything else, I use custom designs (stones, clovers, wooden planks, leaves).
I use mainly the stone path! I like how cool-toned and polished it is. I've got some dirt & dark dirt (campsite & orchard mainly) but love the small town /garden feel the stone path gives me!