What it offers to me that android doesn't is fluid, lag-less, always up to date software, great integration with cloud storage (I really like onedrive integration in WP8 and W8.1, much more than dropbox or google drive (which I never liked)), and offline navigation out of the box (with voice).
I find the UX less cluttered (except settings, they need to organize that a bit), there's only what you need on the screen and nothing more (when it comes to OS and stock apps at least) though lots of 3rd party apps follow this model, which brings me to the next point, nice consistency in user experience. There's pivot, panorama and ... menu, I instantly know how to use a new app. Android was full of iOS ports or just strange looking apps.
I prefer live tiles to widgets, because of consistency. On android some widgets still followed the 2.3 design, some were up to date with ICS (and later) design, and some used something completely different. On WP you either get a nice text on the color of your theme, or on a nice picture or enlarged icon. I like tiles. The only two I would maybe miss are quick toggles (tough I rarely switch anything off, I'd only need it for toggling vibrate and internet sharing (which wasn't available on android anyway)) and a music player controls, but WP solved this in a much neater way.
There are all my personal thoughts and reasons why I'll stick to WP for a while. It still has it's perks (stuff on clipboard disappears after a while, random reboots, excessive heating), but overall I like it.
I also really like the way apps are organized in the 'app drawer+', I find the grid annoying and labels under icons too small. I find an app way quicker on WP then on android.
source: Lumia 925 and Nexus 7 (2012) (and my previous galaxy spica and xperia arc s)