Here u go:

ATTS:
More effective in re-directing torque during cornering
More effective in limiting spin on inside wheel during cornering
Eliminates understeer more effectively
Unique technology

LSD:
Lighter
Cheaper
More reliable
If effective when launching a car
Generally known to have a more natural feel
Is more effective in low traction situations (ie. rain and snow)

Honda test drivers claim about a 2sec improved laptime with ATTS on a ~1.5mile roadcourse(remember that stiffer suspension can also account for some of this difference). Whether that is worth it is for you to decide.