I feel that most Verizon preinstalled apps are pretty mediocre. I think the VZW security app uses McAfee software, which is never rated very high in comparisons. I'd recommend disabling that app, and trying other 3rd party apps like
Lookout or
TrustGo.
There will most likely be people who recommend not using antivirus apps at all, since Android malware is still at the stage where you have to agree to install an infected app in order for it to do damage. But malware does still slip through into the Play Store from time to time, and I feel that it's only a matter of time before malware becomes sneakier and able to cause problems in other ways. So I prefer to stay safe with an app from a company that is known to be on the forefront of mobile security (that would be Lookout for me). Besides, these apps often have nice antitheft and recovery features as well.