Great thread idea.
Power does reside where men believe it to, but obviously there are still conditions that must be met for power to exist. To have power over someone, you must be able to influence them, to have control over them or the ones they care about, or to make people think that you do. The definition of power can change from person to person. Power exists, but it can be manipulated and faked.
I believe here, they were specifically referring to "the afterlife". Arya asked the dying man why he chose not to end his life, and he expressed the fear that the afterlife could be worse than what he is currently enduring. Her quote above is probably influenced by Beric Dondarrion, who told her that (paraphrasing) the afterlife was nothing. It was simply darkness. This probably just reinforces Arya's aethiesm/agnosticism, as well.
Originally, this line from Littlefinger didn't mean much to me. But when I started thinking about him, and how he has risen to power, I ended up LOVING this quote. Tywin shut him down by saying he was pointing out the obvious when he told him that he believes chaos affords opportunities, but that really is central to Littlefinger's beliefs. He has goals, and plans for those goals, but he can't accurately predict how everything will play out. So he causes chaos, and while everyone is focused on other things, he takes advantage of the opportunity and climbs his "chaos ladder". I really do have a grudging respect for the character because of this. It's genius.