The Pc(4380) and Pc(4450) states observed recently by the LHCb experiment were proposed to be either D¯Σc* or D¯*Σc bound states. We analyze the decay behaviors of two such types of hadronic molecules within the effective Lagrangian framework. With branching ratios of ten possible decay channels calculated, it is found that the two types of hadronic molecules have distinguishable decay patterns. While the D¯Σc* molecule decays dominantly to the D¯*Λc channel with a branching ratio by 2 orders of magnitude larger than to D¯Λc, the D¯*Σc molecule decays to these two channels with a difference of less than a factor of 2. Our results show that the total decay width of Pc(4380) as the spin-parity-32− D¯Σc* molecule is about a factor of 2 larger than the corresponding value for the D¯*Σc molecule. It suggests that the assignment of the D¯Σc* molecule for Pc(4380) is more favorable than the D¯*Σc molecule. In addition, Pc(4450) seems to be a D¯*Σc molecule with JP=52+ in our scheme. Based on these partial decay widths of the Pc states, we estimate the cross sections for the reactions γp→J/ψp and πp→J/ψp through the s-channel Pc states. The forthcoming γp experiment at JLAB and the πp experiment at JPARC should be able to pin down the nature of these Pc states.