It's not necessarily better, but it will help you if your data is not really abundant...

For an example, if you look at it as regression, then the model uses your features and tries to figure out how correlated they are with the grade. Your grade is continuous and monotonous, meaning that if the features contribute in "sane" ways to the grade, it will map easily.

If you consider it a classification problem, then each class has basically its own degree of freedom. This could cause your model to be overconfident, whereas with the regression solution at the very least your model is going to try and fit it to a continuous monotonous function.

With the regression task, you are implicitly telling your model that grade 2 is better than 1 and worse than 3. But with a classification model, because each class can be independent, your model can only learn this implicitly through data. Which means that if your data is insufficient for the model to learn it, it won't work, whereas with a regression task, if your data is insufficient, it might still interpolate correctly.