I think Atlanta's first option should be to add to their current roster. Not break it up.
I'd only break it up if I couldn't find a way to move forward with what they currently have.
There is no way for that Atlanta team to be put over the top as currently constituted.
An offer of Josh Smith, Jeff Teague and future draft picks would be a very attractive trade package. Or even switch out J.Smith for Al Horford for a player good enough to warrant it.
I was very disappointed in their lack of trade activity in pursuing star talent trading in recent seasons. Deron Williams, Chris Paul, Carmelo Anthony and now Dwight Howard. I think they could have made a strong offer for any one of them and can still do so for stars who become available in the future.
Or,
As an alternative, trying to trade an expiring contract like Kirk Hinrich + some combination of future picks and/or Jeff Teague for a low level star. Someone who is an above average starter but a notch below All-Star level. A fourth impact guy to go alongside Joe Johnson, Al Horford and Josh Smith.
I think both options are good options to upgrade their current talent base and put them closer to title contention. I prefer each one to a partial-to-large rebuilding movement.