First, if it seems odd that the National Park Service was involved in approving this deal, that is the result of Burns Park having received federal funding in the past.
Second, the land Burns Park is losing, is shown on the map below as the yellow bed. Located on the south side of Charles Boyer Dr. and the east side of the interstate, the land isn't well connected to the rest of the park and is currently unused. Plans call for part of the land to be used for a lodge.
Finally, it is great news that Big Rock Quarry is becoming park land officially. People have enjoyed this scenic area for a long time and it was recently threatened with private development.
I've got photos and other information on the Emerald Park, Big Rock Quarry area at the links below and in the book Trails of Central Arkansas: