Members of both groups wear hats and suits. Both carry briefcases or books. Both have existed for centuries on the periphery of human consciousness. Both take orders from unknown superiors and periodically create unintended consequences when they feel compelled to intervene in the lives of the subjects under their watch.
No wonder the outfits looked so familiar. And casting Mad Men's John Slattery only makes the adjustment team's anachronistic uniforms stand out even more.