If you don't have 3-D secure, then the bank is always at liability, which means that they will be far more prone to not authorise the transaction, which wastes both your and the customer's time. Or the customer might just think that your website is broken or something.
If you have 3-D secure, and the customer passes the check, then the bank is still at liability, but they had the option of verifying the customer by further means. This is extremely useful when the bank is suspicious of the transaction due to transaction size / occurrence.
