Asymmetric multi-cores (AMCs) are a successful architectural solution for both mobile devices and supercomputers. By maintaining two types of cores (fast and slow) AMCs are able to provide high performance under the facility power budget. This paper performs the first extensive evaluation of how portable are the current HPC applications for such supercomputing systems. Specifically we evaluate several execution models on an ARM big.LITTLE AMC using the PARSEC benchmark suite that includes representative highly parallel applications. We compare schedulers at the user, OS and runtime levels, using both static and dynamic options and multiple configurations, and assess the impact of these options on the well-known problem of balancing the load across AMCs. Our results demonstrate that scheduling is more effective when it takes place in the runtime system level as it improves the baseline by 23%, while the heterogeneous-aware OS scheduling solution improves the baseline by 10%.