i personally think bitcoin will overcome Paypal, less fee to pay and no chargeback. Paypal already a well established company but there's a lot of issues and they are not even bother to solve these problems. they will decline and will be gone in 10-20 years
The charge back with PayPal and other businesses that involve banking is a bad sign from the people wanting to steal the customers money even if they have a valid excuse. Bitcoin could get past those scam features and just transact with user to user directly and the customer plus the seller will stay happy when the transaction is completed.
Bitcoin will overtake PayPal if Bitcoin stays alive, there isn't any reason for the project not to do so.
I would agree with your words if bitcoin also broke up and dialed its users at the same pace and amount as paypal, but while the lead in financial transactions remains for the payment system, and not for the crypto currency.