I will tell you the little I've been told, but Cervelo is the correct source to answer this.
If you compare the S5 (gen 2) with the gen 2 S3 (not the 2019) the S3 had a thicker wall structure used to attain likely 95-98% of the strength of the S5 at its price point. I believe Cervelo considered the S3 a great crit bike, tough and robust. The S3 used a less technical, less costly therefore thicker layup than the more expensive S5. I suspect the same can be said of the C3 to the C5. In short the C5 is lighter, maybe very slightly more rigid but likely a thinner wall structure to attain its light weight. Obviously the C series of bikes have very different intent to the S3, ride comfort and stability being a large focus. I have no idea of relative bottom bracket stiffness. Hope this helps
COR Co-organizer 2015
2010 Cannondale Rush MTB
Kona Jake The Snake Cross bike
2011 Cervelo R3 Red - sold
2013 Cervelo S5 Red
2014 Cervelo S3 Red 22