An editorial in this month's Nature Photonics entitled "Transcending limitations" asserts that there are two types of breakthroughs: technological and conceptual. Technological breakthroughs occur when some experiment manages to measure something better or more accurately than in previous works. Conceptual breakthroughs often lead to greater scientific understanding because they force us to look at some phenomenon in a new way.
Often, conceptual breakthroughs require strong patience and steady work to explain previously unexplainable results in an experiment.
I would guess that funding agencies and governments prefer technological breakthroughs because of their immediate economic payoff, whereas academic institutions prefer conceptual breakthroughs.