If you are creating apps for iOS devices, then the dedicated design should be used for specific devices. Separate apps for each device: iPad or iPhone (creating Views can help with that: one document can handle both iPhone and iPad, with different views for one document). The cost is that it requires maintenance of multiple apps.

When creating apps for Android devices, it is better to use unified design for all possible screens. Android is designed to scale for multiple devices. Again, Views can help. The cost of maintenance is low because you have a single app providing unified design. Remember to take advantage of the Fit page option for automatically adapting to different screen sizes:

Apps should have a specific purpose and audience in mind. Mobile functionality should be leveraged, take advantage of its location service, security, cameras, and so on. Mobile apps usually solve problems not solved by other interfaces.

Some testing can be done in a web environment, but true testing requires deployment. That is, not all functionality works on web, for example, map widget, time series widget. In addition, some UI interactions have effects not known until done.