As someone who struggled for two years with an English, and achieved far more in two weeks with a Crane duet, I am convinced that a lot of success/failure with a concertina is to do with the way your brain is set up.
With the English, I could manage chords with the left hand, and to some extent with the right hand. But playing a melody, going left-right-left-right, and moving to different columns of buttons at the same time, and not forgetting to push and pull, it just didn't come naturally, or even with practice.
With the duet, a melody is (usually) all played with the right hand, and on the Crane system the buttons are in a pretty logical (or at least consistent) order.
Not always a practical option, but I would say to anyone who wants to play one, try all three systems if you can (Anglo, English, and Duet) before buying.