Personally, I've felt that Forza has the most enjoyable, and realistic handling; as much as you can experience via pad, between GT and Forza.
GT games of old (I've not yet played a PS4 version) have always had [to me at least], poor handling cars - it's a tough one to put a finger on it, but take the F430 in Forza 2; easily one of my favourite cars, and the car that I drove the most in that version of Forza and the 3rd. I got very used to how the rear end behaved and how to exploit and use it - but jumping into the last GT game on PS3, the car felt like it was FWD and understeered like mad - at also felt quite muted and lifeless.
Again, it's all personal preference, and what I 'feel' and dislike, might please someone else. What I think to be correct, might feel completely wrong to someone else - but for me, Forza has ****** all over GT's handling to date for me. Sure GT looks incredible, and in some ways Forza can look a bit cartoon, but the handling makes and breaks a driving game imo and GT has historically fallen short on that one.
With regards to GT Sport, I've not touched it, nor am I likely too - I have Forza 7 on my Xbone, and Project Cars 1&2 on my PS4, as well as Asetto Corsa - so I have plenty of 4 wheeled fun for now
