I don't have a Fast Sync capable GPU myself, but from what I understand, Fast Sync capped slightly above your refresh rate will not be smoother than using no sync. The point of Fast Sync is not to make things smoother, but to eliminate tearing without the increase in input lag that regular v-sync causes.
V-sync, however, eliminates tearing while making sure that each frame is evenly spaced at your monitor's refreshed rate, so from a smoothness perspective, it should provide the most smooth experience, so long as your frame rate remains above your refresh rate. If it dips below, your frame rate will drop to half your refresh rate, which will not be pleasant. And of course, v-sync causes a substantial amount of input lag, which isn't good for fast-paced competitive games.
With no sync, your computer renders frames as fast as it can, ignoring when the screen is drawing them. This results in tearing, since your computer will switch to the next rendered frame while the monitor is in the process of drawing the previous one, but it also results in the least amount of input lag.
Fast Sync eliminates tearing like v-sync while having input lag that's closer to no sync, but since it doesn't wait for frames to be drawn to the screen before drawing the next, some frames will tend to sit in the queue of rendered frames a bit longer than others, which will result in microstuttering.
Logically, it seems like if the frame rate were limited to a level close to your refresh rate, then fast sync might not cause quite as much stuttering as it would otherwise, but there would still undoubtedly be some stutter due to the pacing of frames getting rendered into the buffer not matching the rate that the monitor is drawing them. Capping fps at around double your refresh rate would likely cut the severity of each stutter in half (assuming your computer could push that frame rate), but you're still going to get more stutter than without fast sync enabled.
Here's one video I found that does a pretty good job of explaining how the various screen synchronization methods work (including G-Sync/FastSync), although it doesn't really go into capping frame rates close to your refresh rate...
https://www.youtube.com/watch?v=L07t_mY2LEU
Also, for the 60fps example video section, you might need to adjust your monitor's refresh rate to 60Hz to accurately see the difference, otherwise it may add a slight amount of additional stutter playing the video back on a 75Hz display.
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