Note: This post is my opinion only. I do not take liability on what you guys decide to do

After a total of 4 track days (2 weekends) I decided to share my thought on the Competitive Mode.
In my case I drove my first weekend with traction control fully on. There's just so many things that can go wrong with a new car on the track. The car behaved well and the traction control did not feel invasive (as long as you drive smooth and don't do anything stupid). I think the TC helps the most in high G corners / hairpins with preventing the tail kicking out. Also it will help if you go full throttle on Track Out too early. If I were you (and I'm not) I would keep the TC fully on for the first couple of days on the track.
On the middle of my third track day I decided to try the Competitive Mode. NEVER change mode in the middle of a session , always start and stick with the same traction setting. I took it easy for the first 20 min session.
I would say that driving on competitive mode is a night and day difference. You can use more advanced techniques such as throttle steering, and faster track out acceleration (as long as you are smooth). For some reason understeer did not feel as bad with Competitive Mode.
If you are feeling that the nanny is getting involved often in Competitive Mode, maybe you should dial back to full TC and work on your line and smoothness.
Have fun and be safe.
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1SS, Black, Black Wheels, A8, MRC, NPP