The complexation between a semiflexible polyelectrolyte and an oppositely charged macroion leads to a multitude of structures ranging from tight complexes with the chain wrapped around the macroion to open multileafed rosettelike complexes. Rosette structures, expected to occur for short-ranged attractions between the macroion and the chain, have now also been seen in recent Monte Carlo simulations with long-range (unscreened) interactions (Macromolecules 2002, 35, 5183). The current study provides scaling theories for both cases and shows that rosette structures are indeed quite robust against changes in the ionic strength. However, the transition from the wrapped to the rosette configuration has a dramatically different characteristics: The short-range case leads to a sharp transition into a rosette with large leaves whereas the long-range case occurs in a continuous fashion. We provide the complete diagram of states for both cases.