We present a comprehensive numerical study of phase diagram and conformational transitions in disordered globular networks with physical/chemical crosslinks. Physically crosslinked random heteropolymer (RHP) networks at positive intersegment interaction dissimilarity, i.e., chi (f)>0, exhibit three globular phases: frozen globular with microdomain structure, random globular, and frozen-random-globular phase, while chemically crosslinked RHPs at positive chi (f) exhibit one random-globular phase and three frozen-globular phases; in contrast with RHPs with physical crosslinks, phase changes in chemically crosslinked RHP networks do not require reentrant passages via a random-globular phase. Based on physical grounds we explain the origins of the phase changes predicted and discuss the order of the phase transitions predicted.