I have both and I am very fortunate to not have had to deal with any large disputes with Amex. I did have one with Chase for around $1k and it was a very painless process.

I will say Chase's CSR response time is addicting. I called yesterday to notify Chase about international travel (A plus there for Amex) and I actually heard hold music for about 10 seconds! The nerve of them to make me wait that long! It also makes me more annoyed when I have to deal with an automated menu for an Amex card that costs 4x as much per year. Also - never had a rep who wasn't based in the US with CSP

As a side note - it seems the CSP rep can help you with your other Chase cards as well. She noted international travel for my Marriott card and answered a couple of questions I had about a particular situation on it. She also told me that if I lost my Marriott card while traveling to call the CSP number as someone would answer faster which I thought was very interesting.