Lots, IMO...
Whether it be from habit (going in one direction most of the time) or physical tendencies (either your right or left arm/leg dominate your body) most mat surfers have a preference going right or left.
For me, the difference really amounts to being able to "feel" while going frontside, as opposed to having to "think" going backside. Frontside is more instinctive, so it allows me to be more sensitive to the wave shape and texture.
Having a frontside on a mat can also be a boon to surfers who are, say, goofy foots standing up, but like to go right on a mat. This can open up a whole new world of wave riding for them. And even if going right isn't their frontside on a mat, if they go right long enough, it eventually becomes their frontside.
There was a guy who used to ride a mat in Santa Barbara who fits this description. His name was George, from my recollection. A goofy foot on a board, and a "left-matter" as well in the beginning, he just kept going right until it felt correct to him. I lost track of him some years back, when he moved to Australia full time.
But I digress...
I actually think that going backside on a surfboard is easier than going backside on a mat, since you use the same rear foot turn on a board, regardless of which direction you go. On a mat, you have to use the left side of your body to go left effectively, or the right side of your body to go right. This demands a complete physical and mental reboot...at least for me.
