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Should I purchase Apple Care and have the Verizon insurance?
Any answer you receive is going to be personal opinion. It's my feeling that if you have the funds and the cost is not an issue for you, then why not protect yourself. Better to be safe than sorry.
Personally, I am never concerned about my iPhone getting stolen because it is almost always on my person, and therefore, Apple Care Plus is all I need. If you are, as stated above by Quis89, then yeah, go ahead and keep your Verizon insurance and purchase Apple Care Plus.