I think there is this luxury where the targeted users, or audience of Baasecamp may actually have the higher end Phones. So the 5/5c or definitely 5S will be fast enough.

But there are an Ocean of cheap / slow and older phones out there, which i dont think they will have quite the same experience if it was in Web compared to Native.

The Gap will shrink, as technology moves forward. But for the best experience around, may be its best to stick to native for now.