The important stats on the three watches are
Invisibility Watch:
9s Cloak Time
Charge time (to full): 33.5s
Recharges 25%, 50%, 100% from small, medium/weapon, and large ammo boxes respectively.
You appear as a team-colored silhouette when an enemy player or weapon hits you.
Cloak and Dagger:
6.6s Cloak Time
Charge time (to full): 15.3s
Recharges while standing still (cloaked).
You appear as a team-colored silhouette when an enemy player or weapon hits you.
Rather than decloaking, you appear as a team-colored silhouette if you move when the meter has run out.
Dead Ringer:
6.5s Cloak Time
Charge time (to full): 16s
Recharges 25%, 40%, 40% from small, medium/weapon, and large ammo boxes respectively.
Does not cloak when activated, but the first time you take damage after activation (right-clicking again before being hit will put it back away).
"Perfect" cloak for the first 6.5s. After that, you appear as a team-colored silhouette when an enemy player or weapon hits you.
Can only be used at 100% cloak.
Decloaking at > 40% cloak remaining reduces cloak meter to 40%.
Louder decloak sound, unless using entire Saharan Spy set.