(Rudy Gutierrez/AP)

Inflation hawks hailed Trichet’s vigilance: “Yes, Americans are now being schooled by the French on how to run a sound monetary policy,” wrote economist Michael Pento. On the other hand, those worried about the euro zone’s sluggish growth argued that the ECB was being run by maniacs. “[T]he ECB makes Ben Bernanke look like William Jennings Bryan,” wrote Paul Krugman. Even if Bernanke wasn’t doing enough to jolt the U.S. economy, Krugman argued, at least he wasn’t as fanatical about stifling growth as Trichet was.

This split view has persisted, even after Mario Draghi replaced Trichet as ECB president in November. The Europeans are seen as overly cautious in the face of crises, obsessed with inflation and willing to tolerate weak growth in the name of austerity. Bernanke, by contrast, has earned a reputation as someone willing to throw the kitchen sink at a financial crisis — even if many economists think he could go much, much further in helping the recovery along. “The Fed has been vastly more aggressive in just about everything,” says Alan Blinder, an economist at Princeton University.

Yet a closer comparison reveals some subtle differences between the world’s two most powerful central banks. Bernanke has been willing to test the boundaries of what the Fed can do in order to preserve financial stability at a time when U.S. political institutions are failing. Europe’s central bankers, by contrast, have been more focused on pressuring Europe’s failing institutions to reform themselves, rather than on circumventing them to save the economy. Here’s a look at the strengths and weaknesses of each approach:

1) Balancing growth and inflation. The Fed has been far more fervent than its European counterpart about slashing interest rates to boost the economy. This partly stems from a difference in the banks’ mandates. The ECB’s main task is to keep inflation low, whereas the Fed, in theory, has a “dual mandate” to fight inflation and unemployment. What’s more, the ECB targets “headline” inflation — a broader price index that includes things the Fed doesn’t fret as much about, like the Libya-related oil spike this year — which leads Europe’s bank to hit the brakes more often.

At the moment, the U.S. economy has recovered to the point where it’s about 0.6 percent bigger than it was before the crash. The euro zone, by contrast, is still 0.3 percent smaller than it was pre-crisis. That’s partly due to the ECB hiking interest rates at a couple of key points during the downturn, including twice this year, even as the Fed is pledging to keep rates near zero for the foreseeable future. (Under Draghi, the ECB has reversed course and cut rates slightly, but analysts don’t expect him to go as low as the Fed has.)

Now that the euro zone is likely to enter yet another recession, the ECB’s tight-fisted approach doesn’t look too good. That said, Bernanke doesn’t get off easy, either. A number of prominent economists have argued that even the Fed has also been too timid and too inflation-averse, leaving millions of Americans out of work unnecessarily.

2) Pumping money into the market during crises. During the worst of the financial crisis in 2008, the Fed began an emergency lending program to keep money flowing through the economy. All told, the bank loaned out some $3.3 trillion to anyone and everyone: U.S. banks, European banks, General Electric, McDonald’s… The Fed also engaged in two rounds of quantitative easing to boost the economy, buying up more than $2 trillion of mortgage-backed securities and other bonds.

Clearly, Bernanke wasn’t above taking unprecedented — and sometimes legally murky — steps to avert a meltdown. “In many cases, the Fed was stretching the law like mad,” says Blinder. (The one big exception was when the Fed concluded that it had no authority to save Lehman Brothers in the fall of 2008.) Even though Europe’s bank often has a lot more flexibility to get involved in open-market operations, Blinder adds, “they’ve been a lot more worried about stretching the law.”

That said, Blinder adds that the ECB also has good reason to be wary of un­or­tho­dox actions like quantitative easing. If the Fed loses money on its purchases, it has the U.S. Treasury to back it up. It’s not clear who would backstop Europe’s bank.

That’s not to say the ECB hasn’t been active — it’s just been active in a different way. Jacob Funk Kirkegaard of the Peterson Institute for International Economics notes that Europe’s central bank has been quite aggressive in lending euro zone banks as much money as they need to stay afloat. The divergence in approaches, Kirkegaard notes, is partly due to the fact that E.U. companies depend more heavily on banks for financing, whereas the bond market plays a bigger role in the United States. “Both banks have been very forceful,” he notes, “but they both face fundamental differences in the systems they oversee.”

3) Getting involved in politics. Rick Perry and other Republicans have slyly hinted that Ben Bernanke has tried to goose the economy to help Barack Obama. The evidence for this is pretty thin. The Fed has generally acted as a lender of last resort — backstopping the economy — with seemingly little regard for politics. By contrast, the ECB has been much more selective in shoring up the euro zone’s troubled states — and, in the process, it has become quite active in E.U. politics, to the point where it has ousted elected leaders.

Consider the ECB’s position in Europe’s debt crisis. There are several countries, Italy and Spain especially, that would benefit greatly if the central bank loaned them money so that they didn’t have to face high borrowing costs on the open market. And, while the ECB has bought up some sovereign bonds — about 185 billion euros worth — it hasn’t been willing to unconditionally backstop the debts of European countries. If it did, it would lose its leverage to push the sorts of austerity measures it openly favors. “If the ECB had gone in two weeks ago and declared openly that we stand behind Italian debt,” says Kirkegaard, “then Silvio Berlusconi would still be in office.”

It’s hard to imagine Bernanke meddling in U.S. politics this way — say, by refusing to cut interest rates unless Barack Obama replaced Tim Geithner. But that’s basically what the ECB has been doing. The defense of the ECB is that it’s probably the only institution in Europe that actually can force structural reforms. But, Kirkegaard notes, the bank is playing “a very clear game of chicken.” By refusing to extend an unconditional helping hand, the central bank can force countries like Italy to rein in their debts. But the ECB is also running the risk of a full-blown financial crisis that brings down the Euro zone.