The Midjay has four intros, four endings, four variations, one break. It only has one button that activates the endings, one that activates the intros, one that does the break and one that activates the fill-ins.
Which intro, ending or fill that sounds depends upon which variation the Midjay is on at the time of the activation. It does not have the "to-end" button, but usually ending four does the same thing.
The SD1 has three intro/ending buttons, plus 3 fill buttons, a break button and the to-end button. Also, the SD1 has the "jump" button which determines whether the intro or ending sounds. I think I probably prefer the way the MJ does it, but both methods have their advantages and drawbacks. The Yamaha method is better, in my opinion.
One other feature of the SD1 is that you can assign vocal harmony changes to the variation buttons if you wish.
DonM