Bigger cars do WAY more damage. To pedestrians, the impact is higher on the body and far more lethal; and to other vehicles, well that's obvious.

I think you're right though, with simplified physics the additional traction does cancel out the additional momentum.

But wider tyres and expensive brakes actually don't make a difference. More contact with the ground just reduces the traction per area, total traction hasn't changed (assuming a smooth road). As for brakes, as long as they're strong enough to lock the wheel, that's enough. ABS helps a little, but expensive designs are only useful if you're in a race.