Is there a way of objectively measuring the efficiency or quality of software or code design?
The abstract conclusion is not really that "some languages are better than others" but that "some languages are better than others for some purposes". Different languages are somewhat like species in evolutionary biology. They have evolved to fill certain niches. There are many evolutionary niches. They have strengths and weaknesses in different areas. Sometimes these types of analysis can degenerate into what is known in stackexchange as "gorilla vs shark" debates.

The question seems to mix up certain distinct areas in CS study. Code quality is measured by defects and is more programmer and implementation related than language related. Defects can be high or low in any language. efficiency in CS is generally considered interchangeable with ("execution") complexity and measured with Big-O notation. There is also another notion of code/ programming complexity where some functionally equivalent implementations may have different levels of complexity in their programs. This is studied especially in OOP theory.

However recently there is some research along the lines you mentioned. There is a large database of programs with identical functions written in the Rosetta code database and some comparative/ objective/ scientific/ quantitative analysis has been done by researchers. See eg:


A Comparative Study of Programming Languages in Rosetta Code / Nanz, Furia
Code length measured in 14 languages / McLoon, Mathematica