I drove both the Lykan and the P1 in a Leagues event, on Swan Village, just now--and the difference in handling between them is huge.
I already knew that the Lykan is much faster than the P1, at least on Mittlack Ride, which is the only track on which I have driven both of them one soon after the other. But I had not noticed their handling before, probably because Mittlack Ride lacks sharp turns or at least has very few of them, whereas Swan Village has lots of sharp turns and no long straight.
The P1's steering or steering response is very fast (if that is the correct term): a little steering input results in a lot of turning. It is much faster than the Lykan's, and seems be much faster than that of every other car that I have driven in the game. It makes it almost undriveable--at least on Swan Village, at least during my several tries on that track. The car would turn too much while taking a turn and crash on the inside barrier, or easily go onto the shoulder in sweeping sections. (Braking might be a contributing factor, the P1's stopping distance being better than the Lykan's.)
In looking at the performance charts the P1 has a steering value of 9, whereas the Lykan has a value of 5. This seems to be a case where reducing the sensitivty is helpful. I will try that tomorrow.