I think you may just have the same issue that I have. I notice tearing, and I notice stuttering, which means I find it very hard to enjoy any game. When I use v-sync on a game that normally runs at 100fps, my FPS is limited to 60/60hz; however, when the game loads an asset or something, the game will still stutter, because it drops from 60 to 58fps for a split second, affecting the frame latency. This issue can be fixed by not using vsync, but looks/feels choppy when the game runs at a higher fps than your refresh rate.
My other issue is that some games have inherrent frame latency issues, such as some of the games you've mentioned. Skyrim, for example, stutters because it doesn't seem to properly implement vsync. I can watch the fps flicker between 60 and 59 (this is just a symptom that's demonstrating frame latency issues), and have to use a frame-limiting application such as Rivatuner statistics server to limit the fps to an actual 60. Some hardware combinations seem to be affected, whilst some aren't.
How to solve these issues? Rejoice, a new age of dynamic refresh rate monitors are about to take over the market. I honestly can't believe it's taken this long for the technology to be implemented, because it really isn't complicated. Gsync monitors, for example, will allow you to turn off vsync and experience smooth gameplay without tearing, which will effectively hide all normal stutters.
You COULD also get a 120hz/144hz monitor, but games HAVE to run at an fps below the refresh rate for the best experience. As soon as they start running higher, the game 'FEELS' stuttery/choppy.
It took me 4 years of frustration, replacing every part in my computer, RMAs, returns, refunds, exchanges and switching brands to realise that my personal issue with stuttering - which seems to go unnoticed by people I try to demonstrate it to - was caused by using a 60hz screen. I suffer from OCD, so that's probably why I notice these issues more, but I really recommend you get one of the new Gsync monitors, or at least try a 144hz screen without vsync turned on.
Edit: I read that you have a 120hz screen. I honestly think you have my issue then. Stutters caused by vsynced game-play simply infuriates you, whilst doesn't affect most people. A lot of people in this thread are essentially getting the same stutters as you, but they simply don't notice them. The number of friend's computers I've used - more expensive than mine, often - that they swear have no issues, I immediately pick up on stuttering. When I try to show them, they either can't see/feel the issue, or say it's "just normal" and "to stop moaning". I recommend gsync, otherwise you may just end up like me and have had a gaming pc for the last 4 years that's cost about £2000 over that time and hasn't even been used.