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Team Owner
Joined: Mar 2001
Posts: 21,325
Likes: 3,841
From: small town in S.E Pa. PA
St. Jude Donor '03-'04
Bilstien's are less aggressive, but offer a slightly better street ride, the trade off , slightly less radial stability.
Bill aka ET
Administrator
Joined: Mar 2001
Posts: 367,775
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From: In a parallel universe. Currently own 2014 Stingray Coupe.
C7 of the Year - Modified Finalist 2021
MO Events Coordinator
St. Jude Co-Organizer
St. Jude Donor '03 thru '25
NCM Sinkhole Donor
CI 5, 8 & 11 Veteran
As E-T says, either will work fine on the car, just depends on how you intend to drive it. I think when I am due for some shocks I will go with the Z06 ones, but that is a long time off. I may change my mind by then. 
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Le Mans Master
Joined: Apr 2012
Posts: 7,784
Likes: 2,255
From: Brighton MI
I went with C6 Z-06 shocks + C6 Z51 sway bars with metal end links on my base coupe. Night and day difference in cornering, but I kept the base springs so the crappy MI roads don't beat me up too badly. 