I haven't used a vertical ladder beam to support a horizontal beam but as TG6 says, I think, in the case where the horizontal beam is connected to the chords of the vertical beam, the inner chord of the vertical beam (closest to the span of the horizontal beam) would take most if not all of the vertical load from the beam.
In the case where the horizontal beam is connected to the rungs of the vertical beam......it could be argued that the rung transfers load to both vertical chords I guess but the welds have to transfer the load.