My paper “Why OSS/FS? Look at the Numbers!” is a massive collection of quantitative studies on free software, with the goal to “show that you should consider using OSS/FS when acquiring software”. It has a large set of different studies grouped into the categories market share, reliability, performance, scalability, security, and total cost of ownership.
If you need evidence, not anecdotes, it’s been the place to go. But it was last updated in 2005, so the latest information hasn’t been included. Finally, a brand-new 2007 edition is available, with lots of additions.