Paul Krugman is absolutely right about this: the Reagan recession doesn't tell us anything about now.
The 1981-2 recession was a very different kind of event from the 2007-9 recession: basically, it was a recession deliberately created by the Fed to bring down inflation. The Fed raised interest rates sky-high, causing a plunge in home construction, which was the main driver of the slump. When Paul Volcker believed that we had suffered enough, he cut rates, housing sprang back -- and it was housing that mainly drove the recovery. Reaganomics was basically irrelevant.The 2007-9 recession was driven by the collapse of a huge housing bubble, and the resulting financial fallout. The Fed couldn't cut rates sharply, because they weren't all that high to begin with; there couldn't be a housing boom, because housing was already overbuilt.
Whether you think the Reagan combination of tax cuts and deregulation worked, there's no reason to think that it worked over the relevant time frame--i.e. that it helped end the recession. The recession was a pretty straightforward monetary contraction, which ended when Volcker loosened the pursestrings again.
Of course, the differences tend to undercut a similar comparison that I've been hearing a lot from Democrats lately: Reagan's low approval ratings, which were around where Obama's are now, but rebounded far enough to win him a landslide in 1984. Unless this sluggish economy suddenly speeds up and soaks up the excess labor force, a better comparison might be Herbert Hoover or Jimmy Carter.