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Both tablets are good for playing music in the background and have apps for doing so.
The Google Play Music app on the left is similar in function to the iPad mini apps on the right. The Nexus 7 app works with the Google Play store and the iPad mini with iTunes.
New York Times in the browser
This image compares the familiar New York Times web site displaying in Chrome on the Nexus 7 (left) and Safari on the iPad mini (right). The advantage of the wider iPad mini display is clearly demonstrated in this image.
The entire Times page is legible without zooming on the iPad mini which is not the case on the Nexus 7.
Photo Gallery apps
The Gallery app on the Nexus 7 (left) has a nice display compared to the Photos app on the iPad mini. Both are similar in functionality.