What is the difference between
<UserControl... in XAML in Windows 8. Looks like both are used as W8 pages.
A Page is what you need to use inside of a Frame to support the standard navigation framework and the standard AppBar class. LayoutAwarePage adds support for different visual states depending on layout (portrait, landscape full/filled/snapped), which really is required when you are building an app to submit to the store.
A UserControl is just a simple way to group some UI pieces and code-behind together useful especially if you want to have a reusable piece of UI that shows up on different pages or if your page design becomes too complicated (eg. if you have a lot of XAML for different page layouts). It is also useful if you want to create a common control to be reused in multiple places or multiple projects, but don't care about being able to restyle it - then you would need to create a custom/templated control.
layoutawarepage are page that allow supports for the various view such as filled, snapped, portrait and landscape. in which you would have to handle the visualstatemanager in xaml and do the switching from various view in codebehind.
while usercontrol are elements that you can place in other pages.