Public key algorithms are heavily used in many digital applications including key establishment schemes, secure messaging apps, and digital signature schemes in cryptocurrencies. Recent developments in the field of quantum computation have placed these algorithms at risk as they enable the implementation of more effective attacks to derive the secret key. Most notably Shor's algorithm exponentially speeds up solving the factoring, discrete logarithm (DLP), and elliptic-curve discrete logarithm (ECDLP) problems. To address this challenge, NIST has initiated a process to develop and standardize a new quantum-resistant public-key cryptographic algorithm. However, asymmetric encryption schemes are known to be computationally intensive, hence energy demanding. The proliferation of energy-constrained internet of things devices, combined with the need to adopt higher complexity quantum resilient cryptographic algorithms, makes it more challenging to continue to use public-key algorithms for all applications. One approach to address these challenges is to adopt symmetric key systems, which are known to be more energy-efficient and more resilient to quantum computers-based attacks. This work performs a comprehensive comparison of energy costs between asymmetric and symmetric key schemes. This comparison is performed using two methods. The first approach uses the energy cost of data usage (ECDU) metric to evaluate the global energy costs associated with internet data usage. It was found that the annual energy consumed by applications associated with public-key cryptography globally is sufficient to provide electricity for 1000 UK households for a year. The second method uses an experimental technique based on constructing a small-scale network of wireless embedded devices. This is subsequently used to compare two key establishment schemes, symmetric and asymmetric, which allows for comparing the computation and communication costs of each solution in a controlled environment, and more importantly estimating the energy consumed by each device participating in the protocol. Our results show that a 58% saving in global energy costs of public key-based applications can be achieved by adopting symmetric key systems. It was also found that a 20% reduction of the energy consumed by a wireless device during a key agreement protocol, can be achieved if symmetric key encryption is used.