Hennie Huijgens wrote a book (in Dutch) where he compared traditional waterfall projects with Agile projects in the same company. Agile projects were on average 34% faster and 27% cheaper than similar waterfall projects.

The link to his website is http://www.goverdson.nl/nl/agile-werkt. He is currently doing his PhD at Delft Technical University, so he will have published some of these results in English somewhere.

Tore Dyba and Torgeir Dingsøyr carried out a review of papers dealing with agile development. Possibly you can find valuable information there, although the paper is more than 8 year old, now. The title is: "Empirical studies of agile software development: A systematic review", Information and Software Technology 50 (2008)

Thank you so much for your answers

More recent papers  on challenges: 

Conboy, K., Coyle, S., Wang, X., & Pikkarainen, M. (2011). People over process: key people challenges in agile development.

Gregory, P., Barroca, L., Taylor, K., Salah, D., & Sharp, H. (2015). Agile challenges in practice: a thematic analysis. In Agile Processes, in Software Engineering, and Extreme Programming (pp. 64-80). Springer International Publishing.

There is this paper: "Towards Pertinent Characteristics of Agility and Agile Practices for Software Processes" (http://www.clei.org/cleiej/papers/v16i1p5.pdf); that has carried out a systematic literature review on characteristics of agility.

It aggregates several studies results and maybe you can find a particular study that fits your need.

You might also find this discussion relevant: https://www.researchgate.net/post/Is_there_anyone_who_can_advise_about_those_case_studies_of_failure_in_Agile_adoption

Thank you for all of your answers, They are great help

You may find relevant our study on agile adoption in Finland. We investigated challenges and benefits of Agile as part of the study.

Rodríguez, P., Markkula, J., Oivo, M., & Turula, K. (2012, September). Survey on agile and lean usage in finnish software industry. In Proceedings of the ACM-IEEE international symposium on Empirical software engineering and measurement (pp. 139-148). ACM.

Here are a few references from my dissertation work on the link between effective teams and software development agility (McKinley, 2015, in press).   Conboy (2009) was the first to formally define ISD method agility.  Through two focus groups, he found that agile methods do not always lead to agility, while non-agile methods may lead to agility.  Similar evidence can be found in other studies provided (Vidgen & Wang, 2009; Maruping et al., 2009; Harris et al., 2009). Here's one of the most recent agile software development reviews (Dingsøyr et al., 2012), Dingsøyr et al., provide an excellent review of the state of agile methodologies, Doing or following agile methods to be agile is the most common research perspective, while being an effective agile team is the other, less common perspective (McAvoy et al., 2012).  My study took a being agile perspective (McKinley).  If you pull these articles, you'll find a wealth of research to help answer your question.

Conboy, K. (2009). Agility from first principles: Reconstructing the concept of agility in information systems development. Information Systems Research, 20(3), 329–354.

Dingsøyr, T., Nerur, S., Balijepally, V., & Moe, N. B. (2012). A decade of agile methodologies: Towards explaining agile software development. Journal of Systems & Software, 85(6), 1213–1221.

Harris, M. L., Collins, R. W., & Hevner, A. R. (2009). Control of flexible software development under uncertainty. Information Systems Research, 20(3), 400–419.

Lee, G., & Xia, W. (2010). Toward agile: An integrated analysis of quantitative and qualitative field data on software development agility. MIS Quarterly, 34(1), 87–114.

Maruping, L. M., Venkatesh, V., & Agarwal, R. (2009). A control theory perspective on agile methodology use and changing user requirements. Information Systems Research, 20(3), 377–399.

McAvoy, J., Nagle, T., & Sammon, D. (2012). Using mindfulness to examine ISD agility. Information Systems Journal, 23(2), 155–172.

McKinley, J. B. (2015). The influence of transactive memory systems on software development agility: An quantitative study of agility (Unpublished doctoral dissertation). Capella University, Minneapolis, MN, USA.

Vidgen, R., & Wang, X. (2009). Coevolving systems and the organization of agile software development. Information Systems Research, 20(3), 355–376,480.

A simple place to start is http://agilemanifesto.org/ . It explains the agile manifesto, its emphasis and advantages.