if I've got it right ,all or most of the chord shapes are the same

According to this article that's less of an advantage than it might sound - partly because the button array isn't (and can't be) big enough, partly because the three-finger system has at least one disadvantage of its own:

"What may not be obvious with the Hayden patterns, but becomes apparent as soon as one starts to play, is that to move from any major chord to another, the same three fingers will be reused, and every finger must (if using the uniform principle, MUST) move to a different button. The same thing is true to move from any minor chord to another. This means that all three fingers must be picked up and put down again in new spots on the Hayden arrangement. If you are playing "block chords"—all notes sounding simultaneously—there must always be a total cessation of sound"

Interesting article. Ironically, what it does for me as a beginner is to persuade me not to look at duets, since the only 'beginner model' I'm aware of is Concertina Connection's Elise - which is a Hayden.