If your company has been using Windows before, you should be first trying to determine any factors that are going to disqualify your company from using Linux. This will give you a quicker answer than trying to go the other way around, (looking for excuses to use linux) Of course, Linux is free, and you are probably going to save your company a bundle by switching to Linux, but if you start by trying to disqualify Linux, you will more quickly find any potential snags that will get your company into trouble down the road. With this information, I'm not trying to say that one OS is better than the other. I'm just trying to give you a more effective starting point. If you find a reason to disqualify linux, then see what kind of open source software is out there that can fill the gap. If you can fill any and all gaps with a solution then you will be able to present your cost-saving findings to your boss.
It's important that you make a list of all of the things that you need to be able to do at your work with either operating system. For example, if you need to operate a print server, or a database server, or you need to type word documents, or make photo publications, etc... You must also consider whether custom software or even custom hardware will need to be used. If you only have the drivers for a particular pen plotter in Windows, then you will need to make sure the drivers for linux can be acquired.