Continuous VS Categorical variable
If your goal is to use them to train a supervised machine learning, the best solution is to find out which one is more efficient in predicting your output.

AGE has more information than AGE_CATEGORY. So, If I were to remove one of them I would remove AGE_CATEGORY.

In Addition, if your goal is to train tree-based models AGE_CATEGORY is not gonna be that much efficient. 

You can use A/B test to find out which feature is more efficient in predicting your output.