You not going to see much of a speed difference in that you are still using the same hardware and it is the same ISP. Where you see the difference is You no longer have to pay yearly subscriptions for Anti-virus nor do you have to deal with virus's, malware or spyware (except for tracking cookies). You also have access to a ton of applications that save you $$$. Also once you learn more about how Linux works you can customize it far more they you can a Windows desktop. You can have multiple desktops installed, I have KDE and Mate currently installed. Also you have multiple work spaces so if you are say researching the history of a tractor and decide you need to write a letter or work on something else you can switch to workspace 2 and you have a clean desktop to work off of. You can switch back and forth if needed. I will actually do the reverse and be working on a document or something and need to look something up on the internet so I will switch to another workspace and then open up the browser and find what I'm looking for. So once you get familiar with Linux you will find a lot of differences.
Since Chieftan was looking at Fedora I thought I might explain a few things about Linux and open source in general. Open source was founded based on the belief that the source code for software should be open for all to see. Companies like Microsoft, Apple, Oracle etc are closed source or Proprietary source code. This normally doesn't affect the normal user just as long as they can do what they want when they want. But just like in our hobby there are purists' who do not want any proprietary software on their system. So there are distro's out there Like Fedora which are designed for those who do not wish to have proprietary software. Also along the same lines there are distro's out there designed for the very technical user like Gentoo, Arch etc. So what I'm saying is if you are considering to explore what Linux is like, as Chieftan is doing, then please go to the distro's website and read about the distro and learn what their target user is. Otherwise you are lible to pick one that might not be suited to your skill and then you will think all Linux distro's are like that when in fact they are not. Linux is all about choice.