This is an interesting chart I found a few days ago:http://www.creditcards.com/credit-card-news/card-complaint-data-cfpb-1282.php
It shows Amex as having the fewest complaints, followed (not that closely) by US Bank, Chase, and Discover. BofA, Citi, and CO are a bit worse.
Wells Fargo, Merrill Lynch, and a few others are not included.
The data are in the number of complaints per $1 billion of transactions in 2012. The disparities are pretty big. There are some mitigating factors, though. CO cardholders generally have lower spending than Amex ones, so $1 billion in CO spending is spread out over a lot more people, increasing the potential for complaints.