Here's the listing of all of the abilities of each rank.
Note - all ranks automatically have the benefits of the ranks below them.

Psykotik

2nd Lieutenant
--------------
No benefits.

1st Lieutenant
--------------
Takes 95% of normal damage.
Accuracy increased 50% while crouching. 
Deals 110% damage.
90% of normal spread on bullet weapons.

Captain
-------
5% chance of not being spotted by monsters.
Player trail coordinates added with less accuracy (10 units).
Deals 120% damage.
80% of normal spread on bullet weapons.
No kick on machinegun.

Major
-----
Adrenaline adds 2 health to max instead of 1.
Twice as fast as previous ranks (as determined by time trials).
Deals 130% damage.
70% of normal spread on bullet weapons.

Lieutenant Colonel
------------------
15% chance of not being spotted by monsters.
Takes 90% of normal damage.
Deals 140% damage.
60% of normal spread on bullet weapons.