Right now this could be a good example. I could tell that bitcoin when compared to an animal is like an eagle while paypal could be the snake. So we already know what would happen when they faced off. Bitcoin is being used around the world and it surpass paypal's daily transaction by 2000% There's no competition at all.
2000% seems such a random number for me. Where did you even get that number? Even when let's say bitcoin ever surpass Paypal's number of transactions per day, it's totally possible that some people are accidentally boosting this number because of the automated pay outs and cash outs on different bitcoin paying websites. Last time I checked, Paypal has got a lot more number of transactions per day compared to bitcoins. I bet it's because all of the major online shops like Amazon and eBay are accepting Paypal while bitcoin is left out. All credit/debit cards can be connected to a Paypal account so most people are using it. While bitcoin, well you have to buy it from the exchanges and most people are afraid to do that. Paypal is just a lot more intuitive or newbie friendly than bitcoin. But today, the population of bitcoin are increasing more and more and people are trying their best to learn about bitcoin because bitcoin allows you to earn money online. I mean, who doesn't want an extra income?
You have some solid points especially about PayPal and Ebay. This bums me out since if you had problems with PP, you dont have a way to use Ebay anymore because EBay is exclusive to PayPal even if they are not one company any more. Why the hell they do not diversify , maybe they have a secret agreement . I do not think that Ebay will go for block-chain ant time soon, they seem as very old fashioned and do not like innovation.