ehm, slightly means "not a huge difference".
The Carbide Spec Alpha can have 3x 120 mm Fans in the front (360mm) for intake, and 3x 120 mm Fans in the back&top (360mm) for exhaust.
My personal airflow rating: (9/10)
The NZXT S340elite can have 2x 140 mm Fans in the front (280mm) for intake, and 1x 120 and 1x 140mm in the back&top (260mm) for exhaust. More Intake than output is very good to keep dust away from your pc. It might be more silent because of the lower RPM 140mm's
I'd give a (8/10) but the front fans might be affected by the near front panel, so it's (7/10).
When you need a 100% performance machine, you're ok with the spec alpha. (I'd take the S340 anyways beacause it looks so good)
Greetings,
Twin-Frozr