What I like about Envoyer is it's close integration with Laravel, I'm sure it could deploy other codebases just as well however I don't think you'll gain much benefit to warrant a move from Deploybot.
I've used both, and I do prefer Envoyer however I have a feeling the support for problems is likely a little strong for Deploybot given what I've read about Envoyer/Forge support of-late.
EDIT: I should clarify my support experience has been good (direct from Taylor) however I had read Forge support was lacking so presume this may be the case with Envoyer.
In case you are still looking for options, there is a new deployment automation tool launched in 2019 - https://deployplace.com/. It's still in beta, but you can request early access.
It's similar to Deploybot, but much faster and supports the deployment of complex applications.