Ok, I'm sick of seeing "Inu-Yasha would win because he's so hot!" So here's an arguement for there side that makes sense.
I haven't seen all of Saiyuki, and I don't know the abilities of Sanzo's Demon Gun or the limit of Goku's powers. However (And I NEVER thought I'd say this), you're all forgetting someone on the Inu-Yasha team. Kagome. She wouldn't last very long if anyone bothered to fight her, but I really don't think the Sanzo team would start on her. They'd probably try to take out Shippo before they considered kill her. That gives her an advantage. Her sacred arrow improves greatly over time, and can probably kill any demon (Other than Naraku, obviously) with one hit. If she could fire fast enough, in theory, they'd be down to just Sanzo. I have some doubt about Goku dying do that whole legend, but we'll say that if he survived, Inu-Yasha could use his Kaze no Kizu (If he was still alive, that is). And if he survives THAT, he should have no problem up against anyone in the universe, making him the all invinsible little monkey boy. Kudos to him.
Sanzo might be harder. Inu-Yasha would have to flee, leaving it to Sango and Miroku. And yes people, Miroku CAN do something other than suck things into his hand. -.-' Sanzo might be a match in one on one for either, but both of them at the same time would be harder. And whether or not Sango is sobbing over Kirara's death is another story... In any case, I voted for the Inu-Yasha team. Though of course if my theory is wrong, they're screwed.