It is not clear if it will destroyed or merely turned into a tool to confiscate wealth, and a better Paypal for the masses. My bet is the totalitarian variant of the future. Click the link above to find out why. Men need a tyrant.
I very much doubt it becomes a "better" Paypal for the masses for the simple reason that it isn't better.
I would be bet on failure over widespread usage of a coopted system. In fact I'd lay significant odds on that bet. (Though failure is somewhat difficult to define precisely -- let's say significant loss of value and usage.)
I see even an oligarchy controlled Bitcoin as better than Paypal, because:
1. Bitcoin is a global politik; and thus even the Chinese mining oligarchy (cum banksters pulling the strings behind the curtain) can't do anything which isn't politically correct globally.
2. Thus Bitcoin will retain many attributes that Paypal as a corporate offering can't provide such as inability to deny any person in any account equal opportunity to access, inability to enforce holdbacks, block certain industries, and other arbitrary shit Paypal does which make my head want to explode. Bitcoin is a trojan horse launched by the global elite to subvert any localized attempt to block/control the shift to digital currency.
3. Thus I predict enormous adoption for Bitcoin, but just remember it will be owned and controlled by the global elite (aka the banksters). And the global socialism will enforce a global confiscation/expropriation of those with wealth, in the coming years. It will be a bittersweet success.