One would hope you'd be decoupled from their rebilling, and therefore could swap vendors more easily.
I actually just ran into the need to bypass Stripe rebill recently. Ultimately a workaround was found, yet sometimes you really just need more control.
It really depends on your usecase, but some benefits:
* Lower cost (just pay for payment processing, not the subscription features)
* Ability to integrate with multiple gateways (to lower cost, support more payment instruments, higher resiliency, etc.)
* More advanced subscription features
* Ability to customize the system through custom code (plugins)
* Data ownership (easier to run analytics reports, since you own the subscription data)