I came from a G25 during GT5P and GT5 days. Then I got a T500RS + TH8RS during GT6, and used it for GTS since launch, till it died on me in January this year. Went straight for the T-GT to replace it, but kept the T500RS pedals, since I already had the Basherboards PU bushing mod for the brake pedal. The T-GT pedals haven't even come out of the box yet.
The jump from G25 to T500RS is huge. It kinda felt like going from a plastic toy to (almost) the real thing. The metal parts, large diameter wheel and FFB strength make Logitech wheels feel light and flimsy. I had it for almost 5 years, running at full FFB strength for almost all games, all the time. I just like my steering heavy n meaty. I thought it couldn't get any better. Till it died.
When switching to the T-GT, the first words that came to mind were "smooth" and "refined". That's probably more to do with the brushless motor (vs brushed in T500RS) than anything else. Both T500RS and T-GT have similar FFB strength, but the T-GT is way smoother, and has less of that notchy gear tooth feeling. I'm also able to feel more of what the wheels are doing, like the onset of understeer from the wheel going a bit light. There just seems to be a bit more communication with the tires and road surface transmitted to your hands. The T500RS has these sensations, too. But the T-GT makes them feel more "high definition", if that makes any sense. The T-GT is also almost completely silent, compared to the noisy T500RS and its fans. They most certainly improved the cooling capabilities, in part with the vents on the T-GT housing.
I've turned down the FFB for the T-GT in an effort to make it last longer. I'm still wary of Thrusmaster quality, even though my T500RS lasted fault-free for 5 years before it died. My T-GT isn't completely faultless...the left analog stick has an annoying tendency to move the on-screen cursor up, even when I'm not touching it. Turning it off and on again seems to solve it, but it reoccurs again pretty often. And before you talk about warranties, I live in a 3rd world country which Thrustmaster doesn't cover, and where consumer rights don't mean jack. But I can live with it.
The T-GT's transducer "rumble" feature feels very light and subtle to me, probably because my homemade sim rig is pretty ghetto, and the table the wheel is mounted on isn't physically connected to my seat. Having said that, I do feel the vibrations through the wheel rim during gear changes, but it's pretty weak. I do wish I could turn it up, but my rig isn't ideal for the vibrations to be felt all the way through.
Overall, I'd say the T-GT is fantastic for GTS if you can afford it. It won't make you faster, but it dials up the immersion (especially if you have PSVR).
[Side note: I haven't tried the T-GT with Assetto Corsa yet, but I remember AC steering feel was fantastic with the T500RS. I expect it to be more of the same, but smoother with the T-GT, since it emulates a T300 in "non-GT" mode. Personally, I think AC steering feel, clutch/brake simulation and overall physics model are superior to GTS. It's kinda like GTS steering feel is with a condom on, filtering and blunting some of the sensations, while AC feels more raw and sensitive, if that makes sense. But that's a whole other discussion
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. There's also rumours and such that pad users have additional driving aids in the background whatever they are but I've no idea.
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(Except atm it's moving the cursor down the screen, not up like yours). I thought maybe I could have damaged it slightly when storing the seat folded down - wondered if it was leaning on it, and since adjusted it so it can't - but sounds like probably not if yours is doing it as well. 
