Interoperability is essential for the commercial adoption of wireless sensor networks. However, existing sensor network architectures have been developed in isolation and thus interoperability has not been a concern. Recently, IP has been proposed as a solution to the interoperability problem of low-power and lossy networks (LLNs), considering its open and standards-based architecture at the network, transport, and application layers. We present two complete and interoperable implementations of the IPv6 protocol stack for LLNs, one for Contiki and one for TinyOS, and show that the cost of interoperability is low: their performance and overhead is on par with state-of-the-art protocol stacks custom built for the two platforms. At the same time, extensive testbed results show that the ensemble performance of a mixed network with nodes running the two interoperable stacks depends heavily on implementation decisions and parameters set at multiple protocol layers. In turn, these results argue that the current industry practice of interoperability testing does not cover the crucial topic of the performance and motivate the need for generic techniques that quantify the performance of such networks and configure their run-time behavior.