1. The migration of your Applications & Dependencies: Let's say you have a bunch of web applications in different frameworks. I imagine you would install your favourite web server and language/framework dependencies, set up their database servers then clone in your applications from their source control, and install any db schemas. You could automate this entire process by using a tool like Ansible to define the entire process in code. It requires a little more investment initially but then in the future bootstrapping your entire stack elsewhere is as simple as running the Ansible configuration on a fresh VM.

2. Migrating Persistent Data: I would probably use a tool like Rsync to move any large data across providers to servers that have been configured as above.

As a Bonus, you could also use Terraform to provision the VMs in the new hosting provider (assuming there's a provider for your chosen company). This can fire API calls off to create the VMs, configure networking etc, then start the Configuration Management tool like Ansible).

Having said that, there's a bit of learning to do to use these tools so I could see some value in a simple tool for migrating VPS'. However, my gut feeling is that you'll need some form of templating/understanding of the changes between the old&new VPS' (even things as simple as IP address changes), so it could be easy to end up reinventing the wheel.