There are many possible reasons for there to be a lack of respect between public, official, police officers and members of private security forces. To boil them down to their essentials, the lack of respect exists because the two groups are somewhat in competition with each other and have stereotyped views of one another.
These two kinds of police forces are, to some extent, in competition. In many ways, they are doing the same job. They often have to collaborate when, for example, a crime is committed within the jurisdiction of the private force. Because of this, and because of organizational pride, they tend to feel that they are competing with one another. (The same phenomenon can often be seen in relationships between local police and federal agencies.)
At the same time that they are in competition, they have stereotyped views of one another. These are often based on a lack of knowledge. Police officers might see private security officers as poorly trained amateurs while they, themselves, are well-trained professionals. They might resent amateurs being dressed in uniforms, armed, and generally looking like “real” police. On the other hand, private security officers might see police as corrupt and lazy bureaucrats.
Because of these stereotyped views, and because of the perceived competition, there has been a lack of mutual respect between these groups.