I took a look at the Time marketing blurb. They actually say " Unidirectionnal braids offers excellent flex characteristics." I agree, but you might as well use black fibreglass or Kevlar which is far more flexible! Moreover a braid is always bi-directional.
As I mentioned in my initial message, woven materials are not desirable in stiffness-critical structures.
The resin/fibre ratio with RTM is lower than prepregs. This means they are heavier.