As mentioned before, it comes down not so much to personal preference, but how you plan on using the device. They both have their strengths and weaknesses.
If you like media (music, photos, videos, etc) then iTunes can't be beat for managing media and letting it handle syncing to the device and managing space requirements.
If you like customizing app screens, widgets, etc. then the Nexus 7 can't be beat.
Some pros for the Nexus 7.
Slimmer, can fit in a big pocket if need be, the iPad Mini can't. This is really important when you need both hands for something quickly.
The Nexus 7 doesn't need a case.
This may be a little more to personal taste, but I don't think the Nexus 7 requires a case, the iPad Mini does. This makes a big difference IMO in overall usable size.
The Nexus 7 is more comfortable to use.
There are also countless iPad Mini Pro's, but the Nexus 7 is a competent device and if you aren't tied to the iOS ecosystem or need strong media management, the Nexus 7 is a better deal