Before answering that question, can someone please tell me whether it is right to compare Bitcoin with Paypal? Because Bitcoin is a currency, while PayPal is a payment gateway which uses other fiat currencies. In an ideal case, we must be comparing PayPal with services such as BitPay.
They are not the same thing, it's like comparing a car with a horse, they might have the both can be used for transportation but they aren't really the same thing are they?
Same thing with bitcoin and paypal, both can be used to transfer money, but they are really the same thing in how they are used.
I can see in the future paypal accepting bitcoin as a currency and working hand in hand with it in the future.