A number of studies have all come to the same conclusion. It's not the execution, it's the legal process.
Almost all death penalty cases are poor people, meaning that the government funds BOTH sides of the case. Both prosecution and defense will have more lawyers, more time, both before, during, and after the trial. More expert witnesses are used by BOTH sides, all on the public tab.
You then add on the extra cost of the legally and morally required, protracted appeals process. The one study I remember specifics was in California, where a figure of $4-5 million per death penalty case was estimated.
This site has a number of studies listed:
http://www.deathpenaltyinfo.org/costs-death-penalty
PS: the person below has no idea what she is talking about.