My money's on the Hulk though. Hulk is fueled by the rage within him, and it seems to be limitless, like mother's love and boring school days. Can Rogue absorb Hulk's rage since it's not a "power" per se? And pretty sure Rogue's absorbing abilities have a limit. Hulk can just get angrier and angrier and go berserk BUT still has some sort of control, poor Rogue would probably go crazy at some point. One happy hug from hulk and Rogue's skeleton is chalk.
Would there necessarily be a fight? Historically the Hulk has not been aggressive towards peaceful, civilian women. If the question is what would happen if Rogue touched him, then the answer would be dependent upon the manner in which it happened. If it was done gentle and calm enough and if she could control the newfound rage long enough, it could sooth him. If she tried to jump him, he'd just knock her out of the way. She'd be back to normal within no time.