The tyres in my Forza comparisons are all upgraded to "sport", since that was the only way of comparing them to GT6 when Forza 5 low longitudinal grip was still a thing. It's much less of a thing in Forza 6. Sometimes in Forza 6 I even feel like I'm trading easier handling (and a little soft-air-ballooniness) against more lateral grip when upgrading tyres.
Anyway, for me it's totally the other way around, I never get consistent lap times in pCARS, I just suck at it and constantly overshoot the apex or spin out because I overdo it on the power-oversteer to correct that... or I brake to late and spin out. Especially in some production cars it feels like the car is not been steered from the front wheels but from a little behind the driver seat. Against AI I always mess up in longer races and when I hear people on GAF say what AI difficulty the play, I feel like a total loser in that game (I know, it depends heavily on the car class and track how good the AI is in that game, but still...).
I don't even remember the Forza 6 Brands Hatch time in the 12C to have been hard for me. I do remember that I treated the Huayra in GT6 like a complete asshole around some turns, because it just couldn't have been so fucking slow compared to Forza (idiotic way of *testing*, I know, I remember to feel a little bad about pushing cars to different degrees when I wrote the lap time down).
Another problem with my list is that I didn't keep track, what patch (and tyre model) the pCARS times where on and neither which of my Forza 6 times where before they patched out the snap-oversteer.
Edit: Saw your Edit now.