Well since HTM only said no Star Mario or ...Gold Sonic (I'm guessing that would be Super Sonic) that doesn't stop the two from using other powers. Let's see we have Fire Mario, Cape Mario, Winged Mario, Bee Mario, Ice Mario, Boo Mario, Spring Mario, Mega Mario, Shell Mario, Hammer Bro Mario, Invisible Mario, or Metal Mario to pick from.
Where as Sonic has his Darkspine form as well as Lightspeed Attack, Speed Break, Time Break, Chaos Control, Sonic Wind, Blue Tornado, Fire Spin, Magical Hands (used in Sonic Adventure 2 to turn enemies into small orbs), Homing Attack, Spin Dash, and of course his trademark speed.
Jak and Ratchet have a ton of weaponry but they can't win here. We have seen Mario survive direct attacks from lightning before and Metal Mario just walks right through it. Sonic's Lightning Shield makes him immune to attacks such as that. Darkspine Sonic would speed blitz him with a speed break attack (able to hit top speed within half a second) and do what he did to Alf Layla wa Layla (Erazor Djinn's transformed state).
Mario and Sonic win this battle! Too bad most of Isle Delfino will end up in total ruin.