Definitely go through AppleCare+. Your deductible will likely be a lot less through them, AND you will retain AppleCare coverage. If the insurance company replaces your phone or pays you to buy a new one, you will lose AppleCare+ and will have to cancel the old AppleCare+ and buy a new one.
(On the other hand, doing that WILL extend your coverage a full two years, if you're concerned about that... it'll just be more hassle and a bit more expense.)
If it turns out your insurance company deductible is less (or zero) than AppleCare+, ask the insurance company if you can submit the AppleCare+ charge to them for reimbursement. The insurance company will look more favorably on covering a $79 than they will the full cost of a $700+ phone, which will factor into your premium costs come renewal time.