I've been using iOS devices since 2008, and never spent much time with an Android phone or tablet. Recently, however, I've been using a Google Nexus 7 Android tablet at work. At first, I didn't really like it. I remember saying to myself, "this feels like a completely screwed up iPad." But as I got used to it, I learned to deal with the quirky and inconsistent UI, various bugs and crashes, and unpolished... everything. In fact, I grew to like a number of things about both the hardware and OS better than iOS. I still wouldn't replace any of my personal iOS devices with a Nexus 7 yet, nor would I recommend it for anyone non-technical, but overall, the Nexus 7 is a very good tablet.
Here's what I like the most:
The size is perfect. I easily slides into the back pocket of my jeans or the inside pocket of my coat. The curved non-metallic back is comfortable to hold with no hard edges. The screen resolution is tight and detailed. The whole tablet feels weightless and indestructible. Unlike my iPad, I don't worry about sliding the Nexus across a table top, and I never use it with a case or cover.
iOS needs this feature. I love having a live, interactive view of both my email and my calendar at-a-glance without having to launch and switch between every app. It's so much faster and more usable than iOS.
Files and App Integration
Perhaps because the OS is "open," the ability to move files between apps and services is really powerful. For example, I can take a screenshot of a game, open the gallery, tap on the image, and send it right to Dropbox. In iOS, I can never remember what services are supported by the Pictures app, nor can I remember if I need to open another app first and then import a picture.
The default email app is somewhat primitive, but I like the full page list view. I especially like being able to tick a checkbox on several emails in this view and mass delete them together. And having the invite and attachment tabs available at the top of an email instead of the bottom saves a lot of scrolling. Again, much faster and easier than the tedious back and forth behaviors in the iOS mail client.
Assuming that the iPad mini form factor has similar advantages as the Nexus 7 hardware, I think Apple could get to parity with the Nexus 7 by adding most of these features to their next major iOS update. I hope they do.