With either of them a customer has the ability to dispute a transaction. With Paypal, the customer has 2 chances, once through the paypal dispute system and once through their card issuer. With a merchant account, the card holder can only dispute a transaction through their card issuer.
As far as pulling money, a merchant account will immediately attempt to pull money from the attached checking account if a card holder makes a chargeback. Paypal will not pull money from a bank account that I have ever seen, you would need to confirm this in their TOS. They do however make the account go into a negative balance if the disputed amount exceeds the balance in the account. Accounts with a negative balance for more than a few days are restricted, and must be brought into the positive before they allow the merchant to continue processing.