Stiglitz lays out his case in Inequality Is Holding Back The Recovery New York Times 01/19/2013. Krugman replies in Inequality and Recovery 01/20/2013.
Without digging into the differences here, I think part of what we're seeing here is that Krugman, despite his sometimes radical-sounding tone (especially among the dimmer lights of many of his fellow commentariat), seems to be much more of a reluctant Keynesian than Stiglitz. I don't mean that in terms of political goals, but in terms of how they analyze longer-term trends. Krugman even says explicitly he sympathizes with the general policy drift of Stiglitz' analysis.
Presumably, they would be in agreement with this part of Stiglitz' argument:
Our skyrocketing inequality — so contrary to our meritocratic ideal of America as a place where anyone with hard work and talent can “make it” — means that those who are born to parents of limited means are likely never to live up to their potential. Children in other rich countries like Canada, France, Germany and Sweden have a better chance of doing better than their parents did than American kids have. More than a fifth of our children live in poverty — the second worst of all the advanced economies, putting us behind countries like Bulgaria, Latvia and Greece. ...Tags: inequality
Even were we able to ignore the economic imperative of fixing our inequality problem, the damage it is doing to our social fabric and political life should prompt us to worry. Economic inequality leads to political inequality and a broken decision-making process.