Bitcoin is different than PayPal so it is like comparing Apples to Oranges when it we're discussing about spending our own money on something. From what I know about PayPal is that they need to have another source in order to get their money. Bitcoin is basically like free money because if someone that knows how to make computers more powerful than it already is, they could build a Bitcoin Miner and get money from Mining Bitcoins and they would get whatever currency they want (PayPal doesn't have that feature).
Bitcoin won't overcome PayPal though Bitcoin will be a popular Digital Payment Platform.
You are right - you do not need to compare these payment systems. Bitcoin is more than a payment system. I am sure that they fulfill their functions and will exist in the future
And actually bitcoins has dominated paypal as a payment method. I am not talking in terms of being accepted by more merchants but actually see this way, suppose you need paypal for bitcoins then everyone would happily give, while doing the opposite is almost impossible unless you are too trusted and ready to pay high fee.
although in previous time when bitcoin was not so much introduce in such time paypal was the one way of transacting money, but now as bitcoin is introducing more and more so bitcoin is becoming the number payment method becoming more and more popular more than paypal. i think in future people will give more and more preference to bitcoin even the big shops will then provide he opportunity to the people to use bitcoin is the the payment methods. i think some countries have already accepting bitcoin for payment method.