Neurons regulate the distribution of signaling components across an extended tree-like cellular structure, using both local and global feedback control. This is hypothesized to allow homeostatic control of the electrical activity of a neuron and at the same time enable normalization of distribution of inputs received from other cells. The performance and robustness of these mechanisms are poorly understood, and are subject to nonlinearities, making analysis difficult. We show that tree morphology places a severe constraint on the performance and stability of a global controller that is alleviated by local action. However, local action reduces the ability of the system to normalize distributed inputs, resulting in a trade-off between stability and flexibility of regulation.