Yes, there is a TL;DR

They currently make no difference. However, previously it would require too much powersliding, which gets rid of ground car control, for all cars before the equalizing, specifically before v1.08 when they "buffed" all the cars like Paladin and Merc. Even then, it still didn't impact the outcome of the game too much. A good player will always be able to lob, aerial, dribble, etc etc with any car. A bad play will not, regardless if they pick the "OP" considered Octane, or pre-patch Backfire.

And they all use the same "handful" because they are used to all of them and it takes getting used to. For example, if I used the Octane, it would take some getting used to of the Paladin's hitbox, considering the Octane's hitbox does not match the model as well as it could. While the Paladin's hitbox matches it very, very well. Even then, the Paladin's hitbox is so low to the ground.

Needing to get used to a car is different than the cars not being able to do the exact same things. Because if a car was OP, you wouldn't need much adjustment to get used to it, switching from a perceived "bad" car. A player used to the previous Backfire switching to the Octane would still require some getting used to do well.

And the differences are being patched to be within a 10% margin because players who don't know the methods to counteract a wide turning radius compared to their used to sharp radius complain.

They do make a difference, hence why they are called differences. However, it's negligible enough that it does not effect the overall outcome of the match.

TL;DR This game is all 100% skill, and the differences in the car don't make the game any easier, prior patch and after patch. A bad player won't play significantly better with a sharper turning car. A good player will always be able to do "X" mechanic to their consistency with any car. A bad player will always be unable to do "X" mechanic regardless of car. Hence it makes no overall difference to the outcome of the game.