The single strand tether climber has the drawback of reduced  payload capacity because the climbing apparatus must also carry the weight of the drive mechanism, motors, solar panels, and associated control circuitry, so that max payload is reduced by the weight of these components.

 With the Better Space Elevator the only non payload weight incurred is the clamping mechanism and associated apparatus used to secure the load to the tether, this weight would be far less that the weight of the complete drive mechanism.

 Due to the motor and drive mechanism being carried aloft on the single strand tether climber the max payload is also limited by the power that can be produced by a power system of an acceptable weight. With the Better Space Elevator all of the drive system remains on the ground and therefore weight is of little to no consequence, this allows an almost unlimited drive power to be applied. The limiting payload factor then would be the strength of the tether and the pull of the counterweight.