I think once Bitcoin is big enough and becomes more stable it has the potential to overcome Paypal. Once outside people start to realize the potential of Bitcoin they will see it more as a currency and be able to treat it like one also.
I don't think that is ever possible as paypal is more popular then bitcoins and it also has more users in compare to bitcoins and even almost all sites accepts paypal as a mode of payment which is totally missing with bitcoins at a moment.