Why using L1 regularization over L2?
Basically, we add a regularization term in order to prevent the coefficients to fit so perfectly to overfit.

The difference between L1 and L2 is L1 is the sum of weights and L2 is just the sum of the square of weights.

L1 cannot be used in gradient-based approaches since it is not-differentiable unlike L2

L1  helps perform feature selection in sparse feature spaces.Feature selection is to know which features are helpful and which are redundant.

The difference between their properties can be summarized as :