This NBER Working Paper says it depends on whether there is competition.
In markets with more hospital competition, going to higher-priced hospitals raises spending by approximately 53 percent and lowers mortality by 47 percent. By contrast, in concentrated hospital markets receiving care from a high-priced hospital also raises spending by 54 percent, but has no impact on patient outcomes.
And the higher spending in competitive markets is worth it:
Such hospitals spend approximately $1 million per life saved. Assuming that the individuals in the research sample live for another nine years, this is cost effective relative to the Environmental Protection Agency’s $8.7 million benchmark estimate of the value of a statistical life.
Unfortunately, the trend in the overall market is for more concentration and less competition.