I'm not sure there is a winner in this case, unfortunately for pets, cars are designed to protect humans in the case of an accident, nothing else.
The biggest issue you have to take into consideration is inertia. When a car comes to a sudden stop, like in an accident, the contents of the car continue to move at the speed the car was going. That's what seat belts and airbags try to solve for humans. The seat belts attach the human body with the car, so when the car stops moving, the human stops too. The airbags cushion the impact of the head and limbs that aren't attached, and still move regardless (Trivia: Neck injuries from the head moving forward while the body stays behind in a car crash is referred to as whiplash).
So what does this mean for dogs? Let's say the dog is in a crate.
- If the crate is not strapped in and the car comes to a sudden stop, the crate will continue to move at the same speed until it comes against something that causes it to come to a sudden stop itself. Then the same process will happen with the contents of the crate (the dog, toys, bowls etc.).
- If the crate is strapped in and the car comes to a sudden stop, the crate will be attached to the car, and therefore stop with the car. But, the contents of the crate will not be attached, and continue to move until they are stopped by the sides of the crate.
Now let's say the dog is wearing a harness that is attached to the seat. They still leave room for the dog to move around, which means there's still room for the dog to continue moving if the car stops suddenly. Especially, since only certain parts are held back in the event of a crash, the issue of whiplash is prevalent.
So then which is safer?
From this very unscientific study, based on my understanding of physics, I would say that a loose crate is the worst out of the three options I listed. A harness is a better option, but still leaves some things to be desired (in my opinion).
In my opinion a crate that is attached to the car is the safest option, because even though the dog is not restrained, the impact has a better chance of being spread evenly throughout the body, rather than at a specific point, which can make a big difference (Would you rather land on your back, or on your arm?). You can also choose a crate with solid walls instead of a wire mesh and add padding to the sides of the crate to make it safer.