Our case was the other way around, Apple TV first, and we are currently working on the iOS app. We have a previous iOS app, but it only knows about alerts. A full dashboard monitoring app was on our roadmap, further down the line, but with the release of the Apple TV (and having the luck of being selected for a developer kit) we decided to tackle the tvOS version first.
This decision was made easier due to the fact that both platforms can run the same code, so most of the API interaction and view rendering code will be reused. It was mostly a greenfield project, because even though we leveraged the knowledge from our alerts iOS app, we took the opportunity of writing everything in Swift, which functional expressiveness makes it slightly more useful when it comes to dealing with APIs.
This decision was made easier due to the fact that both platforms can run the same code, so most of the API interaction and view rendering code will be reused. It was mostly a greenfield project, because even though we leveraged the knowledge from our alerts iOS app, we took the opportunity of writing everything in Swift, which functional expressiveness makes it slightly more useful when it comes to dealing with APIs.