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It takes a little more information to give a precise answer.
"Older" apps, which use XIB, tend to work because XIB for iPhone 5 is automatically scaled on iPhones 6/6+, since the screen ratio (16:9) is the same.
Apps that use the old type of splash screen (Default*.png images) also scale automatically because they are presumed to be made for iPhone 5 or smaller. When you exchange the static screen splash for a XIB or Storyboard screen, is signaling that the app is compatible with iPhone 6/6+ and then issues of different screen size appear.
If you are using those newer screen drawing features (Storyboard, Autolayout), you have to rework the screen design to it to adapt to different sizes by adding constraints. If the screen is all drawn with absolute positions and sizes, it happens exactly what appears in your picture: the interface does not occupy the whole screen. You have to go to relative sizes, based on constraints.
At least this is my experience, comment if your problem does not fit...
Have you developed your app using compatibility mode with other larger screen devices? Try using
anchors
ordock
in their objects.– CypherPotato