Excellent question. How far can private security go with gear vs the police? Lights on cars, what authority do they have? I have no problem stopping and talking to a police officer. A security guard, on a public street, I don't know about that.
Many private security companies have as good or better training than local law enforcement.
As for the lights, it's funny because my company used blue lights when I was there.
Police used red/white exclusively.