Simulation of the transient stability problem of a power system, which is the assessment of the short term angular and voltage stability of the system following a disturbance, is of vital importance. It is widely known in the industry that different transient stability packages can give substantially different results for the same (or at least similar) system models. Due to the usual lack of real-world data in the transient stability domain, in this paper we "validate" the software packages against each other. This is done by simulating the Western Electricity Coordinating Council (WECC) system models in three different widely-used software packages. Two specific approaches utilized to perform this validation are discussed. Also, the sources of discrepancies seen in the results from the different packages are investigated. This enables us to identify the differences in implementation of dynamic models in these different transient stability softwares, and also facilitates some improvements in these packages. In this process, we present certain example transient stability analyses of the WECC system models for different contingencies.