Welcome to OCDO. Remember, we are dedicated (sort of) to the lawful open carry of handguns.
But as such we often run into folks like you cow-orker [sic] (look it up) and discuss how to deal with them.
If the problem is limited to asshat Respek My Ay-Thor-It-Tay behavior complaints to the client (the folks hiring the security company) from the folks he exhibits that behavior towards can have a tremendous effect. Working from the inside, you might look at post orders to see if there is anything about contact with the general public/visitors to the client's site.
If you don't want to risk being a whistleblower ignore his behavior as long as it remains at the level you describe and be the best security guard you can be. Hopefully the client and/or visitors will notice the difference.