The Fed and ECB's goal is not to prop up stock market valuations, but to help the economy by encouraging spending and investment through moderate inflation. The banks are tightly bound by inflation targets. Arguably, the ECB has done too little QE since nominal GDP has barely (or hasn't) recovered in most of Europe since 2007, and inflation has been way under target since the crisis.
It seems like China's reaction is more panic-driven, and doesn't have a framework such as inflation targeting to constrain it. In addition, this intervention is just to prop up stock asset prices; encouraging spending and growth in the whole economy is not the primary goal.
[1] http://uk.reuters.com/article/2010/08/06/us-eu-shortselling-...
It remains to be seen to what affect recent US Fed policy will do long term, however, I would argue that it was definitely a panic driven reaction.
I provide this not in support of China's policy but for context.
Excess Reserves https://research.stlouisfed.org/fred2/series/EXCSRESNS
Overnight Rate https://research.stlouisfed.org/fred2/series/FEDFUNDS/
Federal Reserve Balance Sheet https://research.stlouisfed.org/fred2/series/WALCL
The US government was primarily trying to keep some big companies and banks that were caught in a liquidity crunch from going bankrupt, because them all going under would likely be a spiraling problem. The crisis solution was also rather simple in aggregate...loan them a bunch of money temporarily until they could free up the assets to repay it.
China is currently trying to prop up a stock market that is STILL (even with today's decline), up 50% in a year for no reason. And most trading in the market is done by very jittery small investors (who are also overleveraged and now desperate to get out) rather than big firms and funds. Said small investors are unlikely to be reassured by anything the Chinese government can possibly do. I don't see great chances for the government to be able to stop this from returning to a more realistic valuation.