Would it be cheaper for me to insure a brand new $20,000 prius or a used 10 year old $15,000 range rover sport?

Other things being equal, the Prius would probably be cheaper to insure. Firstly, the moment you drive it off the dealer's lot you'll wipe out 10% of its value, so pretty soon it'll be more or less the same as the Range, so the replacement value will be comparable. But Range parts are more expensive than Toyota's, so repair costs are likely to be higher. Also, the Range is more of a security risk (any would-be car thief will pick it over the Prius any day!), and also is a more powerful car (hence more likely to get into trouble). So yeah, the Prius should be cheaper to insure, not to mention maintain and run.

The only way to know this is to call one or several insurance companies and get some quotes on both types of vehicles.

The fact that you are considering two such wildly different vehicles suggests that you have no idea what you want a car to do for you. Until you work that out, buying would be stupid.

The Prius will be cheaper to insure. It will also be cheaper to run and comes with a comprehensive warranty.

The cheaper to repair or replace the cheaper the insurance premium.

It depends on a lot of other factors. A newly licensed kid would find it costs a fortune to insure a Range Rover because of the potential to cause a lot of damage to other people in such a heavy car.

The used one.