The peace prize stands out for being different.
The economics one stands out for not being endowed by Nobel but instead Sveriges Riksbank well after his death (thus it's the Nobel Memorial Prize in Economic Sciences).
But it's administered by the Nobel Foundation, etc.
The Peace Prize stands out because sometimes it is given to someone who wages war such as Henry Kissinger or Barack Obama.
Giving the prize to Obama, whose main achievement at the time was not to be Bush, was a disgrace and did huge damage to the image of the committee. And he did nothing after that that would have deserved a prize.
Bush's PEPFAR was so good that if they gave him the prize it'd be more deserved than many other people who have it.