I think this goes down to whether or not you allow special items to be floating around the battle arena. Does Mario get to use Yoshi? Does the Red Ranger get to summon his Zord?
Mario
The guy has great athletic ability and keen reflexes, but he can only do so much without his power-ups. These are key in Mario's opportunity to overtake this tournament and produce a shocker. Mario can throw some pretty powerful punches and do some damaging ground pounds, but his moves are often hefty and suspended. Mario will loose the speed/agility battle in this one, but he shines through in a more important area. Being a lone wolf.
Mario often relies on Yoshi in some tight spots, and even teams up with his friends in often times, but Mario has proven to us that he can go it alone against tough foes like Bowser. This is where i believe we see Red Ranger's biggest disadvantage.
Red Ranger (The Original?)
The guy is trained in martial arts and has been known to rival Mario's minion bashing skills with his countless kill count of Putty Patrol. To be honest, if Mario gets a floating star; Red Ranger is done, Zord or no Zord. Red Ranger would be flipped upside down faster than a skinny nerd playing in the NFL. However, if Red Ranger can keep Mario away from the star, or if there is no star at all, Red Ranger nearly has the thing clinched.
Time to tackle the disadvantage. I don't ever recall hearing of a spin off series of one power ranger tackling evil by himself (Unless there is some weird Japanese one that I've never heard about). When you think of Power Rangers, you think of the group. You think of their ultimate finisher as the Megazord. I remember a lot of times seeing one or two Power Rangers trying to take on a foe by themselves and blowing it. Only to overcome the foe with the combined effort of all of the Power Rangers and their complete Megazord. I would even say that over half of those villains were not as skilled as Mario. Mario has a lot of experience under his belt, and multiple variables could swing this match either way.
The Result
I'm going to have to go with Red Ranger on this one. Because I feel like Mario's only chance is with power-ups, and even if there are floating power-ups; what is stopping Red Ranger from getting them first?