If I had to summarize: DAT is more about functionality; Grappelli is a more about style. So whatever fits you, best, go with it. Being a design-driven company, we ended up going with Grappelli.
My company did this analysis when we decided to use Django admin as a client-facing backend for a CMS Product. DAT offers some interesting functionality, some of which is duplicated in grappelli and some of which is not. Grappelli offers a few interesting additions of its own. In the end, we went with grappelli because of the really nice styling. My recommendation is to try both. Early on, we included both in the project, set up their respective dashboards, and it took about 30 seconds to switch between the two.
The commenter is right about grappelli needing to be in sync with django. I made the mistake of upgrading django without checking with grappelli, and it broke several things. The latest version of grappelli supports Django 1.4 and we'll be upgrading them together.