That is pretty much expected. Your plane is receiving more light than trunk because it is facing upwards.
In dynamic lighting solution I would probably advice tweaking normals of the branch to plane to face the same way as the trunk, where branch joins it.
For baked lighting, your choice would be to add 1 edge to your branch plane, about 1/3 from the trunk, and bend the plane, so that the part, further away from the trunk, retains its orientation, and the section, that joins the trunk, does so at lower angle. Adding more taper to the trunks would also light them up a bit better.