I've just played the ATF demo so far, and about 1-2 month of DA. Here is my opinion.
The two are played with a very different scope in mind, in ATF you worry about topography, individual platforms and combined arm tactics. If you are into Tactical engagements, I'd recommend giving a whirl to TacOps 4, a personal favorite (which has a good demo and an awesome umpire interface).
In DA, the challenge lies in careful planning of Intelligence and logistics so hopefully the outcome of an engagement doesn't need to come down to tactical prowess. The interface isn't as sleek as ATF, but the game isn't about the same thing either!
So, ATF or TacOps if you want to worry about how to coordinate strikes and troop movements, manage ammunition levels, etc. The action is limited to the frontline and the airstrikes/artillery models are simplified but great fun. If you prefer a sleeker interface, ATF probably beat TacOps, though.
Go for DA if you want to worry about fighting the battle in both the front AND the rear, plan convoys, manage Intelligence priorities and mess with the Red forces using electronic warfare and Psyops.
I personally think of both as complementary and own both TacOps and DA.
Hope this helps,
Christian