Well, is the new car WORTH more than the old car? Most likely, yes. Did you have collision and comprehensive on the old car? Most likley no.
How much the rate goes up, depends on if there's an actual coverage change, what the rating factors were with the old policy, and what the rating factors are with the new one (your credit could have changed, and you might not have been charged for both accidents at the old policy, AND, you might be adding coverage).
YOUR AGENT can tell you.
But if you had just liability before, and you're paying cash for this new car, then you won't see any increase for the new car - becuase you aren't COVERING the new car.
The safety of the car, doesn't have anywhere NEAR the impact on the rates, as the safety of the driver.