In many situations, both are worth trying. Lasso is good at giving information for factors of interest when one needs individual parameter estimates with some bias included Lasso, because it is a penalized regression technique, attempts to fit better models by shrinking the model coefficients toward zero and the resulting estimates are biased. Lasso is particularly useful for large data sets, where collinearity is typically a problem and for small data sets with little correlation, including designed experiments. Lasso can be used to obtain better predictive models or to select variables for model reduction or for future study.
When in question, consider creating a number of models and using Model Comparison, available in JMP Pro, to compare the models.