You shouldn't be getting ANY Framerate Variation with V-Sync Enabled., as it should be locked to Refresh (or a Lower Multiple there of).
So instead of 52 - 62 FPS, you should have a static 59/60 FPS when the Game is actually rendering at 16.6ms or Lower but will switch to 30FPS when the game is above this.
If you're seeing variation as you're describing then you have V-Sync Disabled or Overridden by the Drivers.
Should this be the case, then said behaviour will also occur regardless if V-Sync is On / Off.
Now this could be because you have Enhanced Sync or FreeSync Enabled., but there is also a possibility that because you have the Desktop set to 120Hz but games are actually playing at 60Hz this can be causing a Disconnect.
I've explained this in another thread about how Digital Displays work, where while you might have the urge to use them at their Full Refresh that it's actually better to either tune the Game to run at said Refresh Rate or alternatively drop the Refresh Rate to the typical FPS you'll see in-game.
I won't got into the technical, but in simplified terms... the further the Frame Rate from your Refresh Rate., the greater the disconnect will be in terms of how the Game Feels BELOW that Refresh. If you get greater than, it actually doesn't matter because the Display won't actually display it although you will get "Screen Tearing" which is just the Display Buffer being unevenly updated over the Frames. Enhanced + FRTC set to Refresh will typically resolve this without actually introducing Input Latency common to V-Sync.
If there are some games that can push 120FPS+ (such-as 1080p Overwatch on Ultra Settings) then by all means set it to Fullscreen Exclusive at 120Hz then set the Custom Frame Rate to 120. This will ensure you can make use of the more fluid gameplay without it being jarring,. but typically speaking I'd still recommend sticking to 60Hz as this is what most Games are Optimised and Default Support.
Also be sure that you're using HDMI (High-Speed or above Cable) or Display Port rather than DVI... as DVI Dual Link might support up to 120Hz, but how it does it really isn't ideal for Gaming because it's splitting it into 2x60Hz Signals, which can often introduce Micro-Stutter, Tearing or Variation if the Graphics Hardware is out-of-sync (which can happen A LOT of Intel Processors., due to their clock variation; on AMD Processors their Static Clocks don't cause this behaviour) ... given this is somewhat limited to Intel / DVI / AMD configurations, and there's no solution to it beyond using a more modern connection (i.e. HDMI/DP) well it could be the cause.
Still it's somewhat difficult to diagnose fully when something "Feels" wrong, given such if very subjective.
Keep in mind switching between Framerates... 120Hz / 60Hz / 30Hz, can be quite jarring and distracting. Especially if you don't game for long enough periods to get used to it. This has become a common complaint on the Microsoft Xbox Forums concerning the One X., as most One X games that are enhanced run at 60Hz while those that aren't typically run at 30Hz, while switching between the two Frame Rates already introduces a Latency Delay that makes them feel more sluggish the 2:1 Frames over 1:1 Frames adds to this sense of Slower Performance because while you can't perceive the Frame Hold, you still Subconsciously notice it until you get used to it.
By switching between Games prior to getting used to it you end up just reinforcing the differences making them more noticeable and jarring rather than having something your accustomed to.
