From 1925 through 1938 Douglas used on most all models a single band expanding brake. Initially semi-servo, though on certain models they reversed the direction of operation nullifying the servo action, though they continued to advertise them as servo! They can range from very poor to very good, with apparently no rhyme or reason. In reality like anything, they need to be setup properly to give their best, or the deck is stacked against you before you even start. Things like having a soft lining, maintaining a minimum gap between the brake band and the drum when retracted, having a circular band rather than a oval shaped one that comes into full contact with the drum when applied, and other common sense maintenance.
The backing plate is a pretty thin aluminum casting, and is not much more than a dust cover, all the brake reaction being taken through the spindle of the brake operating arm and into the frame. The front forks on an EW are not all that rigid either, so everything probably twists and torques when braking, throwing the alignment off from ideal. The 350 EW, and the other early models also used pressed steel brake drums. The drums can 'bell mouth' under braking load, reducing the contact pressure, though the bands are flimsy enough that they should be able to follow suit and conform! Also steel is not as good a material friction-wise, as is cast iron, which Douglas eventually switched to.
But as I said, some folks have reported very light and effective brakes, so they can work well. I have not heard that they were prone to breaking front brake cables.
-Doug