I love asciinema. A key difference between these two tools seems to be that asciinema records a human using the terminal, whereas VHS generates output based on a list of steps to execute.
I can see VHS being nicer than asciinema for a lot of applications, since you can avoid typos and fumbling, and you can easily re-render the same output with different settings.
I've started using demo-magic [1] to automate my asciinema recorded demos, not perfect but it gets the job done. VHS does look excellent however and I'll definitely be giving it a go the next time I need to record anything.