To expand:
What you should think about when using vsync, is that it limits the framerate to multiples of the monitor refresh rate. This means that if you dip below 60 fps, the GPU would discard frames down to 30 fps, to match the refresh rate on the monitor. This is experienced as lag and unresponsiveness, which is why Gsync and Freesync are such godsends.
Another thing to keep in mind when using vsync, is that if you can render above 60 fps, DirectX and OpenGL work differently with buffering. This is why using 120 Hz+ monitors can sometimes feel like you're playing in slow motion (information overflow).
I'm not read up on Vulcan, but here goes for DX and OpenGL (a few years old knowledge, so may have changed)...
The basic difference, is what the libraries tell the GPU to do once they've filled the buffer:
For DirectX, the GPU is instructed to wait until the frame has been pushed to the display, before it starts rendering again. With double buffering, this may mean you get a delay of a few frames from the previously buffered frame (which has been pushed to the front buffer), and the new buffered frame. With triple buffering and badly optimised games, this can cause a jumpy experience, where the game is "ahead" due to computational overhead, but still behind because the buffered frames aren't "up-to-date" anymore. The upside here, is that the GPU isn't stressed to the same extent.
OpenGL is a bit more smart about it, where the GPU is instructed to discard buffered frames if it can render a new frame before fronting the buffer. For double buffered frames, this means that you may still see some artifacts with double buffering, but are rarely lagging behind if the GPU has alot of overhead. With triple buffering you are almost never more than three frames behind. The downside here, is that the GPU is still rendering frames, even when the buffer has been filled, since it'll update the last buffer indefinitely, until it is displayed.
The alternative to this is using fps limiters. This doesn't prevent screen tearing, but locks the GPU from drawing more than X frames per seconds, decreasing the load while still rendering more than enough frames per seconds (if capable).
So tl;dr
For cinematic games, where short dips in fps are less immersion breaking than tearing, enable vsync.
For fast-paced games, where moment-to-moment updates are very important and you always want the most updated information available, disable vsync.
Edit: clarification and emphasis.