120hz advantages
*these advantages are lost when allowing low fps or hitting low fps often
dynamic lower fps swings than your monitor's max rez relying on g-sync to match hz will at least prevent vsync/non-vsync side effects of dipping below your hz (tearing, judder, frame dropping, input lag).

-more recent action shown constantly
 8.3 ms sooner/twice as early at 120fps&120hz, 9.66ms sooner at 144hz,
 while the low fps user's action is "Freeze-framed" a full 16.6ms at 60fps, 32.2ms at 30fps, etc.
 especially useful during competitive/scored games but useful to your survival and performance in any game.

- much higher definition motion transitions yielding higher motion definition animations, increased accuracy/timing/reaction-time, and aesthetic qualities
  again useful for survival but also is a form of image quality.. motion image transition quality and control sophistication quality.

-large blur reductions during your constant FoV movement (50% less blur at 120hz and high fps, 60% less at 144hz, or complete blur elimination w/ lightboost or other synchronized backlight strobing methods)
going back to full baseline 60hz blurs the entire viewport "outside of the lines of the shadow masks" of all onscreen objects, high detail textures, landscapes, depth via bump mapping.
60hz's smear "resolution" during these continual 1st/3rd person FoV movements must equate to a horribly low resolution that is not even definably a solid uniform grid in relation to the material it is attempting to display.
120hz/144hz non-lightboost/non-backlight-strobing still blur but at least it is within the "shadow mask" of all onscreen objects and architecture/geography. All object detail, texture detail, and depth via bump mapping is still lost on the entire viewport.

High definition motion as separate from blur reduction
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Smoothness to me means more unique action slices, more recent action going on in the game world shown - more dotted lines per dotted line length, more slices between two points of travel per se, more unique and newer pages flipping in an animation booklet, pick your analogy. It means less "stops" in the action per second and more defined ("higher definition") animation/action flow, which provides greater aesthetic motion and can increase accuracy, timing, and reaction time.
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Disregarding backlight strobing for a moment.. As I understand it - where a strobe light in a room someone runs across would show blackouts, a typical lcd rather than blacking out just continues displaying the last "frozen" frame of action until it is updated. At 60hz that is every 16.6ms of course, and at 120hz and high fps it would have shown a new state of/peek into the room and run cycle 8.3ms sooner instead of freeze-frame skipping (over what would have been a new state at +8.3ms) to the next later state of the room and run cycle a full 16.6ms later, or longer at lower fps. 30fps would have action slices freeze-framed 32.2ms each while the 120hz user would have seen 4 game world action state updates in the same period, had 4 times smoother motion definition displayed, and would be allowed more chances and sooner chances to input different actions. What is displayed of the entire animated world action in games is updated twice as often(and twice as soon) which can increase accuracy, and in providing more "dots per dotted line" per se, makes movement transitions "cleaner"/aesthetically smoother, providing higher definition movement and animation divided into 8.3ms updates. This goes hand in hand with blur reduction/elimination to make the entire experience a drastic improvement over 60hz/60fps.

Frame rate comparisons

(Of course there could be a much more imperfect timing/rendering of frames than explained below, incl glitches/judders, etc - this is just the raw number comparisons).

30fps would have action slices "freeze-framed" 32.2ms each while the 120hz+ 120fps user would have seen 4 game world action state updates in the same period, had 4 times smoother motion definition displayed, and would be allowed more chances and sooner chances to react to and/or input different actions (adjust trajectories/paths of travel, duck/jump/shoot/initiate defenses, intiate healing, etc).

60fps would have action slices freeze-framed 16.6ms each while the 120hz user would have seen 2 game world action state updates in the same period, had twice the smoothness of motion definition displayed, and would be allowed more chances and sooner chances to input different actions.

misc FPS below 120 would have varying rate comparisons but still would be freeze-framing often compared to high fps at 120hz.

80 fps would attempt to send a new screen update every 12.5ms. On a g-sync monitor, the monitor's refresh rate would drop to 80hz and would actually update the screen every 12.5ms 1:1.
The 120fps+ at 120hz user would be shown 40 more frames in the same period obviously.
The 120fps+ at 120hz user would see frames 1/3 sooner, have 1/3 more motion definition, etc. than the 80fps g-sync user.

Comparing 80fps on a 120hz monitor(non-gsync) to a 120fps+120hz user:
120hz monitors update every 8.3ms. 80 frames sent would leave 40 updates "empty", requiring the same frame to be frequently shown more than once ("freeze framed").
1/2 (40) of the 80 frames would be shown 1:1 at 8.3ms each.
1/2 (40) of the 80 frames would have to be "freeze-framed" to 16.6ms each.
40 "frozen" through 2 updates (80 updates) + 40 at 1 frame per update (40) = 120 screen updates (120hz).
2/3 of the time, the 80fps user at 120hz is seeing 16.6ms "freeze frames" continue through two 120hz+120hz 8.3ms screen updates by comparison.
1/3 of the time, the 80fps user at 120hz is seeing the other 40 frames at 8.3ms.


40 fps would transmit a new screen update every 25ms on a g-sync monitor which dynamically switched to 40hz. That would be the same frame shown through 3 screen updates of the 120fps+ 120hz user by comparion.

40 fps on a 60hz monitor without variable hz (gsync) results in a 40:60 ratio which would mean that:
1/3 (20 to be exact) of the 60hz screen updates would be "un-filled", so would have to be filled with "frozen-frames" through more than one screen update.
These "doubles" or "frame freezes" would be intermixed somehow throughout the 60 screen updates.
20 of the 40 frames could be shown at 16.6ms (1fps per 1hz of 60hz)
the remaining 20 of the 40 frames would have to be shown for 33.2ms (16.6ms x2) to equal 60 screen updates filled (20 through 2hz + 20 though 1hz).
2/3 of the time, the 40fps user at 60hz is seeing 33.2 ms "freeze-frames" continue through four 120hz+120fps 8.3ms screen updates by comparison
1/3 of the time, the 40fps user at 60hz is seeing the other 20 frames at 16.6 ms "freeze" frame through two 120hz+120fps 8.3ms screen updates.

Note: I suppose in the 80fps 120hz monitor scenario you could theoretically have
         60 frames filling 1:1 vs hz and "freeze-frame" 20 frames three times each to fill the other 60hz of screen updates.
         Or in the 40fps on 60hz monitor vs 120hz+120fps scenario, you could theoretically have
         30 frames filling 1:1 vs hz and "freeze-frame" 10 frames three times each to fill the other 30hz of screen updates.
         --- I don't think that is the way it works though, unless it just randomly fills between the two different scenarios and shows screen abberations/judders when not synchronized

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"Personally I want 100fps+ on a 120hz monitor for my games (over 120fps optimally). Whatever my gpu budget is vs how demanding a game is limits what video settings quality i will set a game at. For me, sub 100fps and not running a 120hz monitor is not "ultra" graphics/display experience at all. It is not max settings, "max configuration" nor maximum presentation of the game world to me. 60hz monitors/tv's blur the entire viewport during FoV movement 50% more than 120hz at high fps, and 60% more than 144hz at high fps. Low fps and/or low hz also show half or less the most recent action slices per second, which means lower accuracy//lower motion tracking and lower aesthetic smoothness of motion/fluidity of motion. Maximum blur and the worst aesthetic motion smoothness (and reduced accuracy) is not the best/max visual presentation of a game."