Paypal cannot be overcome by bitcoins because of the simple reason that 90% of the online e-commerce sites accept paypal as a payment method and hence that plays a vital role. Though a person who knows btc and paypal both would always prefer dealing via bitcoins.
If 90% of the people in the world pay for things with PayPal then PayPal has a very large chance in being the top payment processor for online transactions. People that use Bitcoin will see how well PayPal is performing and will try copying it though I am sure that Bitcoin will fail in doing so.
If PayPal integrates Bitcoin into their PayPal system then Bitcoin will be much more popular than PayPal.