Live tiles are not about the flat design, the fluidity of transitions (not being laggy) or the styled animations. These things are just superficial "visual spice".
What are live tiles about? The idea is that any app can display any type of information right on the home screen, and should be able to update that information regularly and in a controlled fashion that doesn't drain your battery. This is a general concept on WP. The WP OS controls the live tiles, but it offers a standardized "socket" into which apps can "plug-in" if they want to determine what the live tile looks like and what data it displays. This is not true for Android or iOS.
Android has widgets, which are similar in the sense that an app can use them to display any type of data directly on the home screen. However, in contrast to live tiles on WP, Android has no control over how widgets look, behave or function. Some view this freedom as a good thing, because it allows widgets to do whatever they want and be more functional as a result. On the flip-side, this freedom also means that widgets are very inconsistent, both in visual style and in how users interact with them. Users must learn how to use each widget individually. I personally value WP's visual and behavioural consistency over Android's (messy) flexibility, but some may disagree.
Apple's iOS has nothing similar.