  We perform a comparative analysis of quintessence and $k$-essence scalar
field models in the data analysis perspective. We study the quintessence field
with an exponential potential and the $k$-essence field with an inverse square
potential in the present work. Before delving into data analysis, we provide a
brief perspective on dynamical evolution on both of the models and obtain the
stability constraints on the model parameters. We adopt Bayesian inference
procedure to estimate the model parameters that best-fit the data. A
comprehensive analysis utilizing Observational Hubble data (OHD) and Pantheon+
compilation of Type Ia supernovae (SNIa) shows that $k$-essence model fits the
data slightly better than the quintessence model while the evidence of these
models in comparison with the $\Lambda$CDM model is weak. The value of the
Hubble constant predicted by both the models is in close agreement with the
value obtained by the Planck2018 collaboration assuming the $\Lambda$CDM model.
