Beyond the parallax effect, what are these new navigation and structural changes? I'm not trolling here, I'm genuinely curious. I'm about to build a new iOS app and I did not see major navigation or structural changes that would drastically affect how I design an app's UI or UX.
That being said, there are a few new things that do stand out:
1) Everything is supposed to be fullscreen as often as possible, with the chrome hiding as much as possible. "Deference to content."
2) Transitioning between view controllers should ideally "zoom" in to new content. Like the calendar app zooming into a day view from a month view or a year's worth of photos zooming into a collection of chronological "collections." In other words, your transitions should communicate _how_ the view controllers relate more than just you're replacing one with another.
3) Text Everywhere. (only new on iOS)
4) More abstract but also more physical (read: mimicking the laws of nature, like physics, rather than mimicking things humans have made, read: skeuomorphism)
There are many more changes, you can read about them in the new iOS 7 Human Interface Guidelines: http://www.slideshare.net/evgenybelyaev16/mobile-hig-2278458...
If I'm building a cross-platform app (or have the intention of going cross-platform eventually), I try to steer clear of any interactions or UI elements that are too obviously from one platform or another.
I really appreciate apps that have their own distinct look and feel which don't use "proprietary" UI features (like the header bar and back button). The most recent app that I've admired is Dots. It doesn't look Androidy or iOSy. It looks like it's own thing. The team behind that did a fantastic job.
If I'm using a news reader or productivity app, I hate having to spend time learning a novel interface. The more conventional the UI, the more easily and quickly I can use it. Unless uniqueness adds a tangible benefit, it's just a pain in the butt.
But hey, it's a (really buggy!) beta.