This paper deals with energy management in smart districts using distributed model predictive control (DMPC). We investigate two decomposition methods, primal and dual decomposition, for problems where a shared resource has to be distributed optimally amongst sub systems. The objective is to compare these two decomposition methods with a focus on how well they are suited in the context of smart district energy management. In primal decomposition a coordinator layer is directly affecting resource limits to the sub problems whereas in dual decomposition virtual prices are used to stimulate the sub areas to change their resource consumption behavior in a desired way. Both methods are demonstrated to be able to converge to the globally optimal energy distribution in simulations, provided that the limit on the shared resource is chosen in a reasonable range. This result is particularly interesting regarding the fact that in the dual decomposition case, the number of degrees of freedom of the coordinator problem is only a fraction of the number of degrees of freedom in primal decomposition.