By subtly using pulses of energy to alter the energy emissions of a ship and disguise them, the Cloaking Device increases the subject vessel's chance of cloaking by 30 percentage points.
(Note that cloaking chances work on a scale of 0-100 - with a Cloaking Device, the 'base' chance is increased, so effectively it's now 30-100, not including skill and ship-size modifiers - this is what is meant by 'percentage points', as far as I can tell.)
The major differences between the two versions is that the Union Cloaking Device is widely available within Union Space, to all Union Pilots of Rank 8 or above, unlike the Neutral Cloaking Device, which requires pilots to have a sufficiently low reputation and know the location of a Hidden Laboratory. Also, it is outlawed in Federal and Imperial space; if you attempt to join either faction with a cloaking device installed, it will be confiscated.