2old, etc.: The BBSxx drives use a cadence sensor for pedal assist. If the pedals aren't spinning, there's no power. Possibly worse, if you're pedaling slowly you get less assist than if you pedal quickly.

Many of the better integrated systems use torque sensing pedal assist: The harder you press on the pedals, the more assist you get.

That explains at least part of the worse pedal assist behavior with DIY hardware.