Is it more expensive to insure a crossover than a sedan?

We are looking at one of each at a car lot. They are selling for roughly the same price. The SUV is actually a crossover, but I'm thinking they will be about the same for insurance. The crossover has more features, though. Don't want to wait til tomorrow (Mon) to get an answer. Want to buy today. Thanks!

I talked to the insurance company today and the crossover was actually a little less to insure. I'm guessing because it is a bigger/safer vehicle. It would probably have less damage in an accident. Interesting.