I am using Qwt now for two years. I like its object oriented classes, which makes it very easy to adapt the plots and functionality. These days QCustomPlot is becoming more and more popular and competes with Qwt. Of course I did compare the APIs. However I am interested in the testimonies of experienced users from both libraries. What is convenient? What not? Are there any pitfalls?
I wouldn't call myself "experienced", as I used Qwt only for a few months, and QCustomPlot for a few weeks. That being said, my impressions are:
EDIT: Author of QCustomPlot is aware of missing functionality to set plot background and promises to add it in upcoming release.
There's also another important difference between QCustomPlot and Qwt - licensing. - Qwt is LGPL, so you can link it into non-GPL project. QCustomPlot is GPL v.3, which many people (myself included) find WAY too restrictive. QCustomPlot author invites to contact him if you want LGPL license.
EDIT2 (25 March 2013): New releases of Qwt branches 5.* and 6.* appeared in November, which annuls "more actively developed" advantage of QCustomplot