Of course Mario's faster than Link; you try running with a big heavy shield, a big sword crafted by a giant Goron, a legendary sword, some 50 bombs, a quiver packed with arrows, a bow to go with it, a Hookshot, a pair of Iron Boots somewhere in your inventory, a pair of magical hovering boots somewhere as well, a few bottles, maybe some bombs that move on their own...
While Mario's got the clothes on his back and the water machine on his back. Which can help him move faster.