As much as I dislike the title, I believe that Balancing Agility and Discipline: A Guide for the Perplexed might contain some information that is relevant to you. This book by two software engineering process and software project management experts - Barry Boehm and Richard Turner. This book looks at various aspects of the agile and plan-driven methodologies, compares and contrasts them, and also discusses integrating them to achieve a "best of both worlds" situation.
Appendix E of Balancing Agility and Discipline contains a wealth of empirical information regarding the costs and benefits of various agile and plan-driven methods. However, there doesn't appear to be any data regarding time effectiveness. But glancing through the data, it appears (as I suspected) that this isn't an either/or choice - some projects experienced decreased effort, faster schedules, and lower defects when applying agile methods. However, other projects that used. The section discusses a number of different projects in different industries, the type of process they used, and what they experienced over the course of the project.
There are plenty of case studies cited in Appendix E that yields this data. There are far too many for me to just start naming randomly, since many are focused in a particular industry or even within a particular organization. If you are going to look at cases, I would suggest finding those that are similar in nature to your team, project, organization, and industry to draw reasonably valid conclusions.
In Rapid Development: Taming Wild Software Schedules, Steve McConnell identifies a number of factors to consider when choosing a lifecycle methodology: level of understanding of the requirements, level of understanding of the architecture, desired reliability, risk management, schedule constraints, amount of process overhead, mid-project "course corrections", ability to provide the customer with visibility, ability to provide management with visibility, and sophistication of the development team and management. There are others, as well, such as organizational culture, so there probably isn't an exhaustive list anywhere.
Even given the exact same project, there is also the team factor. If you take a team that has consistantly delivered software using the plan-driven spiral methodology and throw them into Scrum, they are going to experience a decrease in productivity, an increase in thrashing, and have to overcome a new process model before they can come around to being successful. Even though another methodology might be more suited, there's always the business need to actually deliver the software. That's why process improvement efforts are frequently long-term efforts and not overnight - major changes are shocking to a team and (even if the methodology might be better suited on paper) can cause a decrease in productivity.
There's a lot more than simply effeciency or effectiveness of the process, and you can't simply look at a snapshot of the same team working in a plan-driven environment and an agile environment. You need to consider the industrial and organizational context, the attributes of the project, the team, the customer, and so on when making a decision.
Based on what I read, I'm going to have to disagree with your coworkers assessment. I'm sure that you can find some case study somewhere where an agile project was 60% less efficient with regards to some performance metric than a similar plan-driven project. However, there are also studies that show that agile yields 80% less effort, 50% less time, and high customer satisfaction with the product.