Motivated by the need to reduce computational costs, look-up tables are widely used in numerical simulations of laminar and turbulent flames, for the thermodynamics of the mixture, for detailed chemistry, and for turbulent combustion closures. At the same time, there have been many studies where artificial neural networks have been trained to replace the classic tabulation approach, and their performance against tabulation typically evaluated a posteriori. In the majority of applications the focus is on accuracy, and the objective is to obtain the best network structure which minimises the inference error during training. Computational efficiency however is also important, and criteria are needed to decide whether or not it is worthwhile in the first place to employ neural networks at all, and if so what the potential bounds on the computational time and memory gains (if any) over tabulation are. This is examined analytically in this work by developing scaling laws for the computational cost of tabulation and of neural networks including the effect of network structure. The scaling laws are validated using both model test-data but also data based on a canonical problem which involves inferring laminar flame speeds of methane/hydrogen mixtures at off-training conditions. The proposed scaling laws lead naturally to a framework for effective decision-making between adopting look-up tables or neural networks.