Basic car insurance will cover you for different aspect of an accident. A policy may cover the other driver and car, your car and injuries, and/or damage sustained from 'acts of God'. These would include natural disasters and theft, depending on what your policy states. 4x4 insurance policies will work in the exact same way as regular car insurance, although it may be more expensive. A higher profile vehicle will cause more damage in an accident and will have higher costing repairs.
Another huge factor is that 4x4 vehicles are targeted for vandalism and theft more. This is especially true if you live in the city versus in the country.Since the insurance company has the city as a higher risk zone for theft you will pay more in insurance. It's best to live in a rural area where your high profile vehicle won't be as likely to be targeted.
Costs to fix 4x4 trucks and SUVs are much higher than the cost to fix regular vehicles. This is because parts are harder to find and repair. Insurance companies will look at this as an extra cost to insure your vehicle and will charge you more. If you have extra features added to your 4x4 that didn't come with the stock you will have to get extra insurance to have these repaired in case of an accident. Insurance companies won't voluntarily pay for these extra add-ons unless your policy specifically covers them.
Off road driving is the biggest difference between 4x4 and regular car insurance. This option lets you take your vehicle off of the road and through other terrains. If you damage your vehicle, which is fairly likely, the damages will only be covered if you have a specific policy with off-road insurance. A standard policy will become void for the time you drive off road, leaving you to pay the damages yourself. Prices will increase if you regularly participate in races or other all-terrain sports with your 4x4. Some people choose to get insurance for these events just for one day to reduce costs.
Aside from the fact that 4x4 vehicles are more expensive to insure, the policies are not all that different from regular cars. Get your best quote by searching multiple car insurance companies online. Read through each policy offered by the companies before committing to one, since some include features that others don't.