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I think Comp mode loosens up the active handling a little. Both modes do have the TC off. Maybe someone else can verify this.
That may be the difference. The "Competition Mode" my C5 Z06 saved me a couple times but scared me also. Once I had an extreme tank slapper going entering the E-Way in third gear. I thought I was going around, couldn't catch up on the steering. I heard the brakes working and the active handling straightened me right up. It got pretty loose but didn't go around. It got loose enough to cause a pretty good pucker. The 150 shot got the Z loose a lot. I never ran in "Traction Control Off" mode in the Z to feel the difference. In fact not really sure it had that mode.