In order to perform material decomposition for a three-material mixture, dual-energy CT (DECT) has to incorporate an additional condition, typically the prior information related to certain physical constraints such as volume or mass conservation. With the introduction of photon-counting CT and other multi-energy CT (MECT) platform, more than 2 energy bins can be simultaneously acquired, which in principle can solve a three-material problem without the need of additional prior information. The purpose of this work was to investigate the impact of prior information on noise and bias properties of three-material decomposition in both DECT and MECT, and to evaluate if the prior information is still needed in MECT. Computer simulation studies were performed to compare basis image noise and quantification accuracy among DECT with prior information, and MECT with/without prior information. For given spectral configurations, the simulation results showed that significant noise reductions can be achieved in all the basis material images when prior information was included in the material decomposition process. Compared to DECT with prior information, MECT (N=3) with prior information had slightly better noise performance due to additional beam measurement and well preserved spectral separation. In addition, when wrong prior information ([-2.0%, 2.0%]) was intentionally introduced, the quantification accuracy evaluated by root-mean-square-error (RMSR) using MECT with prior information was less than 1.5mg/cc for gadolinium quantification and 1.2mg/cc for iodine quantification.