The true picture is that America does spend significantly more on defense than most developped countries - about twice as much. It also spends quite a bit on health care but its people get a very poor return on that spending while private sector health care does very well out of it. I have no idea how education spending compares across countries.
As for what AEI or the WSJ do - well it does remind me of that study 'showing' that people in Mississipi are better of than Swedes. But I'm really not convinced that their quality of arguments about Europe are a model to follow.