Depends on what recipe you are making
According to local tradition if you are making something like the lemon bread you want the coconut a bit drier so you use more mature coconut and grate, not shred. Other recipes might be "wetter" so you'd use young coconut and mash to add to fillings, etc. When I actually shred fresh coconut I use a very fine shred blade on my big FP or I shred by hand to get the thinnest possible results.