The dramatic growth in demand for mobile data service has prompted mobile network operators (MNOs) to explore new spectrum resources in unlicensed bands. MNOs have been recently allowed to extend LTE-based service called LTE-LAA over 5 GHz U-NII bands, currently occupied by Wi-Fi. To support applications with diverse QoS requirements, both LTE and Wi-Fi technologies introduce multiple priority classes with different channel contention parameters for accessing unlicensed bands. How these different priority classes affect the interplay between coexisting LTE and Wi-Fi technologies is still relatively under explored. In this paper, we develop a simple and efficient framework that helps MNOs assess the fair coexistence between MNOs and Wi-Fi operators with prioritized channel access under multi-channel setting. We derive an approximated close-form solution for each MNO to pre-evaluate the probability of successful transmission (PST), average contention delay, and average throughput when adopting different priority classes to serve different traffics. MNOs and Wi-Fi operators can fit our model using measurements collected offline and/or online, and use it to further optimize their systems' throughput and latency. Our results reveal that PSTs computed with our approximated closed-form model approach those collected from system-level simulations with around 95% accuracy under scenarios of dense network deployment density and high traffic intensity.