Before anyone on PC jumps in about it being "X using mod Y", please keep this topic to only the standard games and the way they can be played. Thanks.
The handling in an open world and free roam racing game is always a hot topic. You have your casual players who like nothing more than being able to easily hit the roads and fields and have the car behave in a controllable manner, then you have the in-betweeners (simcaders?) who like a little bit of fight with their vehicles but not too much that understeer and oversteer make them panic, and then you have the simulators, who like nothing more than a truly authentic experience. (and would probably wish for real fuel consumption, tyre wear and the need to wash and wax your car after every outing :p)
Forgetting all about those different types, it needs to be remembered that the driving in the game itself is the core of it all, and if it's crap, then it doesn't matter how big, detailed and jam-packed full of features it is, as you're not going to have much fun when playing through it if the handling annoys you. You might be able to endure it enough to make it through, and perhaps the tuning, modification and photo mode features or whatever else is available, are so enjoyable that they themselves take over.
But it's the game's world that matters most, no? And if you can enjoy it as well as all of the extras, then a damn good game you have found
Now, not every game is going to have everything you want, and I am only asking for the game that in your view had the best driving feeling, for you, and to briefly say why it was the case.
In my opinion I still find it hard for any game to beat the feeling of the original... Forza Horizon. There was a nice balance between all the different drive types, the frightening speed through monster power, and the feeling of weight and inertia displayed by the vehicles. I got to try FH2, and FH3, but only briefly, and I did not like the way it seemed to have regressed and felt a bit more floaty than their oldest ancestor. Was FH too close to FM for some and so they dialled it back?
The Rally Expansion also is a clear indicator of why I rank FH as the best, the feeling of the car tackling those routes and struggling for traction, Scandinavian flicking, bogging down at points, and the pulling off a perfect handbrake turn was just glorious.
If you can, I really recommend you check it out and judge for yourself.