While I have moved to an iPhone as my daily driver device, I keep hopping to my WP device; I just like the live tiles concept.
One of the great advantages of the live tiles is the ability to deep pin in an application. For instance one may pin a ticket that was booked via an app to the home screen. The concept is nice, but the issue is that even system apps do not support it properly or consistently and I have always wondered why. One typical use case is messaging application, where I would like to have the ability to pin a conversation thread directly to home screen. This is very useful especially for a SMS thread or a single SMS from say IRCTC that gives ticketing information. Currently it is very messy to search for that one particular SMS. It would be very handy to just pin that SMS thread or a particular SMS to home screen.
The same applies for the email client was well. These are some simple things that would bring more consistency to the OS. For for those who are overjoyed with the introduction of notification center in WP 8.1, no notification centers do not solve every problem on earth.