There are winners and losers in every transaction, and that is what this is, a transaction. I'm sure that Braves management has studies the costs and risks in detail, but a couple of things that instantly come to mind for me are:

1) Traffic. 7:05pm games on Mon-Fri, specifically.
If you are coming from Gwinnett down I-85, then once you get inside I-285, you have lots of options to get around the Grady curve.
At the new location, Mon-Fri games just got near impossible to make. How early are you expected to leave Gwinnett at to make a 7:05pm game when you use I-285?

2) Downtown businessmen/workers - 7:05pm games on Mon-Fri, specifically.
Again, if you work downtown, you can get off work, and shoot over to Turner Field quickly. Traffice going up I-75 to Cobb gets backed up in rush hour, and will only get worse.

3) Hotels/restaurants/neighborhood - big plus moving to Cobb

4)East Cobb - The Braves management is moving to where there is the most emphasis on baseball. Look at the Lassiter/Pope area, almost every park seems to have 4 or more baseball fields.

5) City of Atlanta - City management has proven their ineffectiveness at managing and developing. They had the opportunity to build up the area around Turner Field during the boom years, yet did not accomplish anything.

6) Season ticket holders - no one on here appears to be a season ticket holder.