The heterogeneous cloud radio access network (HCRAN) is a promising paradigm which integrates the advantages of cloud radio access network (C-RAN) and heterogeneous network (HetNet). In this paper, we study the joint congestion control and resource optimization to explore the energy efficiency (EE)-guaranteed tradeoff between throughput utility and delay performance in a downlink slotted H-CRAN. We formulate the considered problem as a stochastic optimization problem, which maximizes the utility of average throughput and maintains the network stability subject to required EE constraint and transmit power consumption constraints by traffic admission control, user association, resource block allocation and power allocation. Leveraging on the Lyapunov optimization technique, the stochastic optimization problem can be transformed and decomposed into three separate subproblems which can be solved concurrently at each slot. The third mixed-integer nonconvex subproblem is efficiently solved utilizing the continuity relaxation of binary variables and the Lagrange dual decomposition method. Theoretical analysis shows that the proposal can quantitatively control the throughput-delay performance tradeoff with required EE performance. Simulation results consolidate the theoretical analysis and demonstrate the advantages of the proposal from the prospective of queue stability and power consumption.