I've had to use both the $24.95 Amex insurance and CSP insurance for little issues. Both were able to get the job done, but Chase was more work on my end.

Amex - caught a pretty large rock that immediately cracked the windshield of a rental car in Germany. The rental return immediately noticed it, and I was charged 700 or so EUR for repair and loss of use, on the spot. Amex mentioned this would happen and recommended I dispute the charge while going through the claim process. The claim process was easy - I sent Amex copies of all of the paperwork, a photo of the vehicle and damage, and a month later the issue was resolved.

Chase - ran over a raccoon or something running across the highway and destroyed the front bumper of a Camry. While Chase did eventually cover, I had to pay National's initial estimate of repair+loss of use (refunded later) and chase National around for a few weeks for paperwork.

If I'm renting internationally (especially if I'm not good at the language) I'll use Amex, otherwise Chase will get the job done.