Bitcoin is not competing with Paypal or Visa its competing with the US dollar. So in a sense the relationship between Bitcoin and Paypal is like the Trojan horse and Troy. If we get bitcoin inside paypal, then that will be a big blow to the US dollar.
I agree with your statement. Bitcoin and Paypal are two completely different things and Bitcoin can only complement Paypal as another mode of payment ... So, the question should really be "Will Bitcoin overcome the USD or some other fiat currency?"