Is there an advantage to antibacterial soap?
Short answer: There is no benefit for their use in households. 

Long answer: These soaps (see here for the complete list) contain the so called quaternary ammonium compounds Benzalkonium chloride and Cetrimonium chloride which indeed have antimicrobial properties.

While they do not promote resistance to these compounds (see reference 1), their use is still not recommended, as their permanent use might dry out the skin, can cause contact allergies and the products released into the environment are also problematic.

There are two studies, which compared the use of normal soap (which has some antibacterial properties on its own) to antibacterial soaps in household environments and found no differences. See article linked in reference 2 for a summary and references 3 and 4 for details on the studies.

This doesn't mean that antibacterial soaps are useless at all, they simply make no sense in households. For hospitals or doctors they are an important tool to protect their patients before operations. But here detailed instructions for how long and how the hands have to be washed are provided. Hand washing is also followed by another disinfection step, which helps with efficiency. But this is very much different from the way people wash their hands at home. See reference 5 for some opinions here.

References:


Use of germicides in the home and the healthcare setting: is there a
relationship between germicide use and antibiotic resistance?
Plain soap as effective as antibacterial but without the risk
Consumer antibacterial soaps: effective or just risky?
Effect of antibacterial home cleaning and handwashing products on
infectious disease symptoms: a randomized, double-blind trial.
The Burning Question: Is It Safe to Use Antibacterial Soap?