mobile - when designing an app for both Android and iPhone, should the user interface be the same?

When designing a mobile app for use on both iPhone and Android, should you make the UI the same on both platforms? Why or why not?

I have thought about this a bit. To some extent, this entails more work, because the UI kits are not the same, so you have to do more custom programming. On the other hand, it might save you work in designing documentation or doing user support.