As far as what you think any particular study "proves," you need to look at more than just the conclusions presented by some abolitionist study. You need to analyze the underlying methods and assumptions.
"In a recent, widely cited study of death penalty costs in Maryland by the Urban Institute, one-third of the cases eligible for the death penalty were resolved by a guilty plea. Yet the study’s estimate of costs makes no allowance for the possibility that percentage would drop sharply if the death penalty were repealed. Study commission reports in New Jersey and California have similarly ignored the issue or made inadequate allowance for it.
“The fact that these studies have omitted an important and obvious factor raises serious questions about their credibility,” said CJLF’s Legal Director Kent Scheidegger, the author of the study. “What else did they leave out?” To take just one example, both the Maryland and California studies calculate death row imprisonment costs on the assumption that inmates sentenced to death will live out their natural lives in prison."
https://www.cjlf.org/releases/09-05.htm