When Harry meets Frodo

As the sun sets down over the hills of Hobbitton in the Shire, and a bespectacled boy looks out the window of the Griffyndor common room, the greatest and most fearsome creatures of darkness, in two different worlds but no less evil for this fact, are doing everything in their power to find and destroy them. How would a meeting between these two relatively unimportant (well not really so unimportant in the case of Harry), small, relatively defenseless characters be?

What would they say to one another? Would the conversation be of ordinary things like the weather, or flowers or owls, or some less common but to them just as ordinary such as Quidditch or elves? or would they sit down to discuss the burden of having the task of saving the world? Would they compare notes on how to be a hero?

All of this is assuming they have already gotten over their acquaintances, and explanations of their own peculiar worlds. One of the most likely outcomes of such a meeting would be a deep sense of relief on the part of both of them, for finally they would have someone to understand them in a way that no one else will ever be able to; after all, only those burdened with the fate of the world on their shoulders can really understand what it feels like, not just the delusion that you are going to save the world, but the brutal knowledge of it being a given fact, and that should you fail the result would not be just a disappointment for those who believed in you, but most likely their deaths would be in order. Talk of a way to screw up one's mind!