Just looking at current roster constructions and "holes" given the teams mentioned in the potential three-way deal (projected salaries per MLBTR)...
White Sox Get:
Samardzija - $9.5 million
Gattis - $650,000
Eaton, Ramirez, Abreu, LaRoche, Gattis, Garcia, Viciedo, Gillaspie, Sanchez
Sale, Samardzija, Quintana, Danks, Noesi/Bassit/Rodon
Why It Works For Chicago - Samardzija gives them the staff a contender needs (and has made no attempt to hide the fact that he loves Chicago and would be open to signing an extension to pitch there for either team), Gattis gives their offense a huge boost (and really doesn't even downgrade their defense behind the plate when he's back there). An Abreu/LaRoche/Gattis middle of the order would provide them the offensive fireworks to keep up without just about everyone.
Athletics Get:
Upton - $14.25 million
Johnson - $6 million
Minor - $5.1 million
Crisp, Lowrie (2B), Upton, Moss (RF), Butler (DH/1B), Jaso (DH/1B/C), Johnson, Norris, Gentry
Gray, Kazmir, Chavez, Minor, Griffin/Parker/Nolin/Graveman
Why It Works For Oakland - Upton replaces Donaldson's production, Lawrie slides over to 2B to give them a huge upgrade there, moving Reddick and Vogt in the same deal helps clear up their glut of corner guys, Minor provides insurance in the event Griffin or Parker don't regain form.
Braves Get:
Reddick - $3.7 million
Vogt - $650,000
Pomeranz - $650,000
Renato Nunez
Tim Anderson
Francelis Montas
(2016/2017)
Peraza (CF), Anderson (2B), Freeman, Nunez, Reddick, Vogt, Simmons, Bethancourt
Teheran, Wood, Miller, Pomeranz, Hale/Jenkins/Montas/Sims/Hursh
Why It Works For Atlanta - Clears $20.95 million in salaries to chase Lester or Moncada with, lands 2B (Anderson/Peraza), 3B (Nunez), and CF (Peraza/Anderson) of the future and adds more arms in the same deal. Stockpile building now includes true high-upside, almost ready guys in Jenkins and Montas. Their presence (along with Sims and Hursh) should allow the flexibility to target high-upside high school arms in the draft if they so choose.