Lots of variables there, both cities have cheap areas and expensive areas. Are you talking about just the differences that apply to each whole city? (Tax rate and electric rate and such)
I am talking about what can be compared apples to apples, with the assumption that some cannot be so compared. With those, I assume there is a logical equivalent or something close enough to use.
What are your biases that would need to be addressed so you would accept an analysis as "true"?
Businesses all over the world use lots of various economic development metrics that report cost of living in various cities that use the same equivalent analysis and metrics for each city from a macro or average standpoint. Are you looking for something that also looks at the micro level of extremes rather than the means?