I find the newer story of the death of the trees to be somewhat weaker. In the earlier one, where Melkor pierces them and Ungoliant sucks out their light and life, it's far more explicit that this is a deliberate attempt to destroy the bliss of Valinor. Of course, the story may have evolved that this wasn't his actual motive, and that Ungoliant was merely to be a distraction while he went about his real work - stealing the Silmarils. But somehow having Melkor as the prime mover in the death of the Trees is - to me - a much stronger and more coherent device.
Regarding Ungoliant, I tend to view her as a "neutral" Ainu. One of those who desired Arda and went down into it, but didn't ally herself with either side. In that sense, her motivation is personal gain, which certainly fits with her character as described, as she is not concerned with nor interested in specifically doing evil, but merely with satisfying her lust for light. She certainly would have the whole world for her belly!