CFD simulations are reported to compare hydrodynamic/axial dispersion in a classical helical-shaped and planar serpentine-shaped tubular reactor at a millimetric scale (1-5 mm) for the first time. A two-step simulation approach is validated against experimental data on residence time distribution in serpentine coils. The method is then used for parametric analysis to explore the impact of geometric parameters on the coiling factor and axial dispersion coefficient. Dean vortices in the coiling region are visualized. The findings from the parametric analysis are utilized to develop empirical correlations and Artificial Neural Network (ANN) models for estimating coiling factors and axial dispersion coefficients in both serpentine and helical coils. The absolute average relative error (AERR) in predicting the coiling factor is 3.5% for helical coils and 4.6% for serpentine coils. The AERR of the ANN model for predicting the axial dispersion coefficient is 14% for helical coils and 10% for serpentine coils. The study reveals that both axial dispersion coefficient and pressure drop are higher in serpentine coils compared to helical coils. Axial dispersion is found to be relatively unaffected by pitch (helical) or bend diameter (serpentine) and tube diameter but shows significant reduction with a decrease in pitch circle diameter (helical) or gap between bends (serpentine). The developed correlations and ANN models can aid in the precise sizing of tubular reactors designed as helical or serpentine coils. This is exemplified through a case study involving the synthesis of an ionic liquid, where the helical configuration demonstrated a performance advantage of approximately 6% over the serpentine configuration.