Lisa is right, if you only want to measure efficiency vs. novelty as dominant attribute of models, you can rely on Zott/Amit:
Zott, C., & Amit, R. (2007). Business model design and the performance of entrepreneurial firms. Organization Science, 18(2), 181-199.
Zott, C., & Amit, R. (2008). The fit between product market strategy and business model: implications for firm performance. Strategic Management Journal, 29(1), 1-26.
Both papers provide a comprehensive list of scale items.
However, if you really want to distinguish business models based on their key dimensions, you need to find a different approach. My recommendation is to define the business model framework that fits best to your research and try to find validated scales for each of the dimensions that you need to fully capture the business model.
I know that a few scholars are working on comparable approaches. I currently have three papers under review that are based on my operationalization. Unfortunately, none of them is published yet. Patrick Spieth to my knowledge has also a paper on the operationalization of business models in the pipeline, but I do not know about his progress.
A third idea would be to start a real scale development project. I think if you follow the prominent approaches for scale development like the one of Churchill and carry such a project out with high methodological rigor, you could develop something really interesting for the BMI community and would certainly get cited a lot.
to get an idea about the best fitting business model framework for your research I can recommend Massa/Tucci with Business Model Innovation (book chapter; The Oxford Handbook of Innovation Management).
It depends on what you mean with quantification... I understand your question in the way that you want to compare business models in an industry, which does not necessarily mean that the study itself has to be of quantitative data. E.g., if you want to build BM typologies you can also use qualitative data, like Amit and Zott 2001.
In our study we did 18 case studies to map the possible characteristics of industry specific BMs for the diagnostic industries and finally send out a questionnaire to 100 companies in this sector with these different characteristics. The aim was to identify BM clusters. In the end we got a “business model landscape” for the German diagnostic industry.
If you plan something similar, than I can recommend an overview of typologies and taxonomies in BM literature, which is published under the following link and contains a literature review from a conference paper, I presented in 2012.
http://www.varietyofinnovation.org/?p=473 “The Art of Constructing Typologies and Taxonomies of Business Models“ with the literature overview table here: http://www.varietyofinnovation.org/wp-content/uploads/2014/02/Table-1-Overview-and-characteristics-of-typologies-and-taxonomies-in-the-business-model-literature.pdf
If you think in BM and quantitative dimensions like Thomas, I know this dissertation from Uni St. Gallen about “Management of Art Galleries–Business Models“, http://www1.unisg.ch/www/edis.nsf/syslkpbyidentifier/3927/$file/dis3927.pdf
even if the initial question was asked already some time ago, a recent publication of mine might be of interest for empirical business model researchers. I just got a paper entitled: MEASURING BUSINESS MODEL INNOVATION: CONCEPTUALIZATION, SCALE DEVELOPMENT AND PROOF OF PERFORMANCE accepted in R&D Management Journal. I will upload a full text on my profile soon.