While they all work in a similar way, there are definite variations in the end result. The canvas will give you a bit more texture if only taken to 220, the linen gives a higher/tighter finish especially if taken past 400. I like using canvas for that reason, for a working knife, espeically a big one, you can have a handle that is smooth to the touch but gives a small degree of texture that actually increases when wet (my guess is the open canvas material swells a bit when exosed to moisture).
There are also differences between the different canvas micarta types. If you can find some old stock "industrial" grade micarta it is tougher/harder/denser then the current micarta being made.
I had some old black canvas micarta that was found in a scrap yard. This stuff was much more dense/heavy then the current black canvas that is being sold at the knife suppliers etc. It almost worked more like G10, but was definitely micarta..... Wish I had a ton of that stuff!!