First, the New iPad (with Retina Display). Because of the different aspect ratios, you can see that widescreen video playback on the Nexus 7 is actually pretty similar to what you get on the iPad. The long dimension of the screen is only an inch or two shorter, and the width is pretty much the same as letterboxed video you get on the iPad.

For the most recent Kindle, the width is pretty much the same, although the Nexus 7 is a little longer. I'm perfectly comfortable holding the Kindle with one hand when I use it, but I'm finding that it's a little difficult for me with the Nexus 7. If I hold it too vertically, it starts to slip out of my hand. Definitely easier than an iPad, though.

I still have my Kindle Keyboard, which I don't use so much anymore as you can probably tell. The Kindle Keyboard is slightly shorter than the Nexus 7, but slightly wider.

Now for the 3rd dimension. The Nexus 7 is thicker than all 3 of the devices I'm comparing, but not significantly so. When using them, I can't really tell that the Nexus 7 is any thicker.
iPad

Kindle 4th-gen

Kindle Keyboard

At this point, the Nexus 7 is definitely going to replace my iPad. I can't tell any difference between the retina display on the iPad and the Nexus 7's display. Text looks just as crisp on either device. The speaker on the Nexus 7 sounds better as well. I'm still unsure whether I'll stop using my Kindle, though. I wish the Nexus 7 was a little easier to hold with one hand. I'm going to try to use the Nexus for reading for a few weeks and see if I get used to it.