The proliferation of ubiquitous communication with the Internet of Things has led to advancement in wireless communication technologies. Today, they have become an indispensable component of smart city applications thanks to the lower cost and easiness of the installation and the maintainability. For example, they are a promising alternative of the wired solutions used in Smart Grid Advanced Metering Infrastructure (AMI) networks. However, wireless communication networks are more vulnerable to cyber-attacks and easier to be eavesdropped, so researchers have proposed a number of secure protocols. In addition to being vulnerable to cyber-attacks, AMI also exposes consumer power data which poses privacy issues. While there has been a lot of research to address these issues, the validation efforts mostly utilized simulators and actual overhead due to these approaches have not been captured in a realistic setup. Therefore, in this paper, we chose two open-source wireless mesh networking standards, IEEE 802.11s and ZigBee, and built an AMI testbed at FIU Engineering Center that will be able to collect power readings from smart meters. Then, we used the testbed to assess and compare the performance of the two standards under fully homomorphic encryption and secure multiparty computation-based privacy-preserving protocols that can provide computation on the encrypted data. Extensive experiments under a variety of conditions indicate that IEEE 802.11s-based wireless mesh networks are more suitable for the AMI networks when used with a reliable transport layer protocol at the expense of data collection completion time while ZigBee can be a viable option for protocols that generate relatively far smaller data packets.