If you look at the formula for acceleration (a = ∆v/∆t) and acceleration force (F = a⋅m) the only two things we can truly influence here are speed (slower collisions are less dangerous) and time (collisions where the force transfer takes longer produce less force).
The latter is what makes the difference between getting hit with an cushion and an equally heavy rock. The same difference exists if you run against a brick wall and against an angled grassy hill (or: a bendy car hood). Not only will the elastic hood (and the roll) absorb part of the collision energy, the angle of the hood stretches the acceleration over longer time and reduces the force transfered on your body.
So if you get the choice as a cyclist, the choice is pretty clear.
Newton's 3rd law, implies the more mass you have the less recoil you feel.
For example hitting a massive box will hurt a lot more than a light box, because light box will get some acceleration of its own vs massive box.
One thing it would definitely affect tho is the time within which the car could brake, provided they react in time.
That claim right there is begging for a source. It's hard to imagine landing from a person's height is worse than hitting a brick wall moving 40 km/h, unless that brick wall also threw you more than 6 meters up into the air, which point at which you'd be moving faster than 40km/h when you hit the ground.
As another example, here's a locally-high-profile crash [0] (the driver, a city councilwoman and the daughter of the county commissioner, left the scene and didn't report the crash for hours). Red lights and sightlines aside, even though not much momentum is imparted to the cyclist, the crash was enough to flip him over and knock him into the air, which changes all of the calculus for landing damage from what normally happens when you fall off a bicycle. If you land straight down on your head, it might be worse for you than getting hit in the torso at a higher speed.
[0] Content warning: this is a video of someone getting hit by a car https://youtu.be/X7V_H9bADDM?t=54