Insurance companies consider the likelihood that a particular brand of vehicle will be stolen, vandalized, or involved in an accident. Companies use different systems and reporting agencies to derive their vehicle symbol. This can be an ISO symbol or a proprietary symbol based upon cost new and/or type.
In addition, insurance companies look at industry wide statistics as well as their own experience with claim payouts to calculate the rates. Each of these factors go into deriving a statistical rate for insurance.
SUVs aren't typically in the top 10 list of most stolen vehicles, so that factor is not as large. The simplest insurance factor to look at is cost and size. A vehicle that costs more to repair after an accident (physical damage coverage) or can inflict more damage (large SUV) when they have impact (property damage liability) will be a higher risk than smaller, less expensive vehicles.
The cost to insure an SUV is generally 15 percent more than the average car because of the greater cost of repairs in a property damage liability claim or medical damages (bodily injury). Another factor that most people don't know is that
SUVs don't have to meet the federal government's standards set for bumpers on cars, relative to parking lots and commuter traffic. So, even though they are bigger they really aren't safer.
To specifically answer your question, yes a larger SUV will cost more to insure than smaller SUV. Among similar sized SUVs, those with higher safety features and lower cost new will be cheaper to insure.