As far as I can tell, Bitcoin has three main benefits -
No government / no chargebacks
Very low transaction fees
Bitcoin, like gold, isn't issued by a government. There are pros and cons for government issued currency.
Bitcoin, like cash, doesn't have chargebacks. This benefits sellers at the expense of buyers (I know there is technically a way to reverse a Bitcoin transaction but I haven't seen it in practice).
The standard 2.9% plus $.30 transaction fee is fine for expensive items but for micro payments (anything under $1) the fees are too high. Sell something for $1 and 30% of your profit is gone. Sell something for $.30 or less and you are losing money.
There are a lot of business models for services at a dollar or less. Whatsapp was selling it's messaging service for $1 per year. In the recent past selling for so cheap would be unthinkable. Thanks to mobile phones, Whatsapp has 450 million users. That's $450 million in just one year. Credit card fees would take $135 million while Bitcoin would take closer to $0 (let's not talk about app store fees).
Credit card fees pay for banker salaries, reward points, and chargebacks. If we can reduce credit card rewards (like in Europe) and if our credit cards had better security (like in Europe), credit card fees can be reduced dramatically.
Another benefit of Bitcoin is it can go to the 8th decimal place so for example, the New York Times can sell an article for .00001 Bitcoin which is less than one penny. The only reason the dollar stops at $.01 is because the penny is the lowest physical currency. Physical currency - paper bills and coins, are only 2-3% of currency. The dollar is digital and can be divided as many times as needed, even to the 8th decimal place.
Moving money from one bank account to another in America takes 2-3 business days. Our system for moving money is based on bankers hours even though money is digital. We literally turn the computers off at 5:00 PM and on weekends.
Bitcoin doesn't have this problem. Bitcoin transfers are instant. There are so many businesses that can be done when transfers are instant. Let's say your business generates $100 in a day. Waiting 3 days for your money to hit your bank account means you have to wait 3 days to reinvest. In our perfect business with no expenses and a 10% profit margin, if we reinvest every 3 days, we will have $260 in a month. If we only had to wait one day for a money transfer, we'd have $1,745 in a month.
Time is money and in this case Bitcoin wins. Except, you don't have to wait 2-3 business days for a bank transfer in Europe and Canada, their transfers are just as fast a Bitcoin, instant.
#1 is good for goldbugs and libertarians. As long as governments have a monopoly on nuclear weapons, taxation, and prisons, our money will come from them. Or as Barry Ritholtz says, since fiat money is worthless, send it to me and I'll dispose of it for you.
#2 and #3 transaction fees and transfer times are an American and third world problem. Europe and Canada have solved these problems but American currency doesn't compete with other currencies in a meaningful way. That is why I am rooting for Bitcoin. Perhaps Bitcoin can show bankers and regulators that instant transfers will mean more transfers. More transfers mean fees can be lower because they will be made up in volume.
I, like so many in the tech world, believe a digital currency will take over. I believe we already have one, the Dollar. It just has to improve.