As it stands the deduction and credit have the same income requirement however this was not always true and may change in the future. It used to be that the deduction had a higher income cap and that is why many adult student used it instead of the credit. So since there is no reason to use the deduction alone, when would you use it?
The reason for using the deduction is when you are spending more than the $10,000 cap for the credit. This could happen if you have multiple students using the lifetime learning credit, either in graduate school or if you are taking more than four years to finish school because of working.
The idea is to count the first $10,000 towards the credit and the remaining expenses towards the deduction. This will save you the most money on your taxes.