They're exactly the same interface and software wise, except some apps are displayed in tablet mode, which is usually better but sometimes worse. Another difference is also that in landscape, the virtual buttons are portrait on the right on Nexus 5 and on Nexus 7 they are landscape on the bottom, wasting precious screen height. These virtual buttons are the only thing I hate about the Nexus 7, after removing them with apps in the Store, you gain a lot of screen space. However, Nexus 5 is 16:9, while Nexus 7 is 16:10, so the visible screen is more or less the same in the end.
I mostly use it in portrait mode because of that.
As I said, that is the only thing that bugs me about it. Otherwise, it's a great little tablet, great size for watching movies, series on the go (or in bed), it should play all games available in the Store and do all other unproductive things you can do on a tablet.
I had a 2011 Xperia Arc S before, and with it's single core CPU it quickly failed to play latest games, that's why I resorted to the Nexus 7.
Nexus 5, however, is newer, has the latest hardware and is capable of playing anything you throw at it, so getting a Nexus 7 is really only for extra screen size, but it does pay off. Maybe diagonal isn't the best measure, try screen area:
Nexus 5: 69 cm^2
Nexus 7: 142 cm^2
So the screen is actually double the size of the Nexus 5, and it's noticeably bigger when watching videos.
If you're going to mostly use it to watch videos, get the N7, if you're primarily going to surf the internet and read documents and such, I'd recommend you to check out the 8" tablets LG Pad 8.3 and Samsung 8" (tab or note), both come with buttons on the side and therefore have more vertical pixels (both 16:10).
Then there's also 2013 Nexus 7, with latest chip and 16:10 fullHD but it's quite pricier then its 2012 brother.
Why would you need a tablet for anyway? If you want it because it's popular, then forget about it. If you have other reasons, write them down, it's easier to recommend that way.
Nokia Lumia 925 16GB
Nexus 7 32GB, 4.4.2 stock, rooted, Xposed installed
Sony Ericsson Arc S, 4.0 .587, rooted
Dropbox for you: http://db.tt/Qk80xRg
500MB extra for both of us.