We did both for the first time last fall on the dining plan.
They were our 2 most expensive meals on the plan.
DH ordered filet mignon at both. He thought CR's was better. We had 2 extra people with us at CR who also ordered filets, and enjoyed them. Everything at CR was good, but our favorites besides the filets were the beef skewer appetizer, tilapia, and the Chocolate Wave dessert (which we consider to be the best we had at wdw). The kid's Build your own sundae was really cute.
At CSH I also had the filet, and it was good. The onion soup was really good. The chocolate lava cake wasn't near as good as at CR. CSH has kid appetizers, CR did not. We were offered really yummy smoothies, but I think they stopped doing that. DD was given a glow cube, but I think they stopped that also. Kids can get a steak here - DD loved that. The kid's brownie sundae was cute & really big - DH "moped" that DD's dessert was actually larger than his.
We're returning to CR on the next trip, so that's our favorite of the 2. I would highly recommend CSH too though - sorry, I know that doesn't help you decide.
IMO the atmosphere at CR is a plus.