I figured this was a worthwhile thread to have, now that all Atma choices are out on the table. Keep in mind that all the statements I make are relative to my gear, targets, and normal support. Your mileage may vary.
Always Atma:
Atma of the Razed Ruins - Ironclad Pulverizer - 50 DEX, 30% Crit rate, 30% Crit damage - The strongest Atma
Atma of the Gnarled Horn - Sobek - 50 AGI, 20% Crit rate, 10 Counter - A nice mix of defensive and offensive stats. AGI contributes to reducing monster TP gain and Evasion.
Third DD Atma:
Atma of the Apocalypse - Shinryu - 15% Triple Attack rate - Technically our best third DD Atma. Quick Cast certainly has its perks, as does auto-reraise.
Atma of the Dark Depths - 4 Salvage bosses - 20% Crit rate, AGI/Eva - Comes out ~2% worse than Atma of the Apocalypse and offers a lot more durability. I suspect the "minors" in the description are wrong.
Random other Atma:
Atma of the Earth Wyrm - Dragua - 100 Earth resist - Useful for resisting earth (Tunga/Glavoid/etc.)
Atma of the Future Fabulous - WotG missions - 50 MDB - Useful for soloing things that do a lot of magic damage
That's all I've got! Can anyone think of others?