I've got both cards and have traveled all over the world with them. I'm not giving up my Amex ever. They've saved my ass in big and small ways so many times and I just don't trust Chase to do the same.
I do love the way the CSR looks and feels though, and it's essential to have a Visa or MasterCard when traveling as so many places only accept those two.
Chase is doing great, I will keep both for the foreseeable future. It's going to take time to completely steal me from Amex though, they've been doing right by me for more than 10 years.