Quantitative easing has had a difficult time stimulating demand (which would put pressure on prices and raise inflation). The money mostly piles up in banks instead of turning into new loans and new spending. Helicopter money would, I think, do much better, especially if it was distributed to people with a very high propensity to spend the money (so it would have much better distributional consequences as well). But central banks seem afraid to try this, or even consider it seriously. Simon Wren-Lewis says those fears are unfounded:
Central bankers and their irrational fear: Mervyn King said
“Central banks are often accused of being obsessed with inflation. This is untrue. If they are obsessed with anything, it is with fiscal policy.”
As an academic turned central banker, King knew of what he spoke. The fear is sometimes called fiscal dominance: that they will be forced to monetize government debt in such a way that means inflation rises out of control.
I believe this fear is a key factor behind central banks’ reluctance to think seriously about helicopter money. Creating money is no longer a taboo: with Quantitative Easing huge amounts of money have been created. But this money has bought financial assets, which can subsequently be sold to mop up the money that has been created. Under helicopter money the central bank creates money to give it away. If that money needs to be mopped up after a recession is over in order to control inflation, the central bank might run out of assets to do so. A good name for this is ‘policy insolvency’. 
There is a simple way to deal with this problem.  The government commits to always providing the central bank with the assets they need to control inflation. If, after some doses of helicopter money, the central bank needs and gets refinanced in this way, then helicopter money becomes like a form of bond financed fiscal stimulus, but where the bond finance is delayed. In my view that delay may be crucial in overcoming the deficit fetishism that has proved so politically successful over the last five years, as well as giving central banks a much more effective unconventional monetary instrument than QE.  But central banks do not want to go there, partly because they worry about the possibility of a government that would renege on that commitment.
The fear is irrational for two reasons... [explains]...
Central banks overcame one big psychological barrier when they undertook Quantitative Easing. That was the first, and perhaps the more important, stage in ending their primitive fear of fiscal dominance. They now need to complete the process, so we can start having rational discussions about alternatives to QE.