From what I understand, there should be no real difference between Windows 7 and Windows 8.1 in gaming. You may run into a few driver or compatibility problems with Windows 8.1, but there are usually fixes for those. There's no performance boost with Win8.1.
Windows 8.1 was very polarizing for a couple of main reasons. The first, is the huge departure from the classic Windows start button. Many people hated this. Second, Windows 8.1 has a lot of ways to do more than one thing. The new UI was confusing for people and often didn't make sense.
Personally, I prefer Windows 8.1 to Windows 7. Windows 7 is still one of the best operating systems, I just feel Windows 8.1 makes more sense.