I'm going to guess that the tree on the right uses alpha-blending (instead of alpha test / mask, or no alpha)?
Alpha-blended textures force objects to be sort dependent, which means they are rendered after the scene, and, therefore they can't cast shadows.
This isn't a HeroEngine issue, this is a standard, "how modern graphics depth buffers work" issue.
Assuming that's the case, change the texture format, or use SpeedTree
Cheers