While there are a couple of benefits of collision insurance, the main one is that you can file a claim and receive reimbursement regardless of who was at fault. Collision claims usually get processed faster than property damage claims because the insurance company does not have to spend time investigating who was at-fault. Another benefit is that you only deal with your own insurance company, rather than another insurer with less incentive to pay for your claim. Collision insurance can also be used toward your rental car in most cases, which can spare you from having to buy rental car insurance.
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Comprehensive car insurance covers damages from an "act of God," or events that are not caused by a car driving into something else. An "act of God" can include things like damage from a heavy tree branch falling on your car. Since you have no control over when or why a tree branch would fall on your car, this kind of accident would be covered under your comprehensive policy.
The key difference in collision vs. comprehensive coverage is that, to a certain extent, the element of the car driver's control. As we have stated before, collision insurance will typically cover events within a motorist's control, or when another vehicle collides with your car. Comprehensive coverage generally falls under "acts of God or nature," that are typically out of your control when driving. These can include such events as a spooked deer, a heavy hailstorm, or a carjacking.
Policies typically use vague language when referring to acts of terrorism, but they are generally insured by the comprehensive portion of your policy. For example, if there is an act of terror and you need to make a claim on your car, that can only be made if you have comprehensive coverage. Since some circumstances are out of our control, comprehensive insurance is certainly important to have in your policy.