In regards to the question: Does Polysporin have advantages over soap
It doesn't contain a notable claim.
The asker says "Some highly regarded sources" but it only provides one source. The chosen quote from that source is:
Soap can irritate the wound, so try to keep it out of the actual wound.
As though soap is being discouraged in place of Polysporin. But this is incorrect. In the same article it says:
Thorough cleaning reduces the risk of infection and tetanus. To clean the area around the wound, use soap and a washcloth.
So there is actually no source for the claim that Polysporin is either better than soap or should be used instead of soap.
The question is also asked: "Does Polysporin have anti-bacterial or other properties that are not found in soap".
Searching for the individual contents provided by the asker and also linked from the product website, you can find many reliable sources that say these ingredients have confirmed anti-bacterial properties. So there is nothing to say here.
I suggest this question be closed as not a real question as there isn't an actual notable claim.