TL;DR: In my opinion, Bitcoin success depends mainly on beating credit cards, paypal and alike as a way to buy stuff online. It's unclear whether it will beat them. Read more to see why.
Where Bitcoin has no future
I'll start pointing out that Bitcoin is a bad idea as the currency of any expanding economy. Being deflationary is a bug, not a feature here, as it encourages hoarding rather than spending.
The rest of this piece is about how without being the currency, Bitcoin might still be a currency. Not being the currency means that BitCoin it is unlikely to work as a Unit of Account, that is, the stuff you compare other goods to. Like, you know, the way you price the milk you buy in U.S dollars for U.S people, Chilean pesos for us Chileans and so on, depending on where you live and the name of such local money.
However, money has many functions and Unit of Account is just one of them. The other two very important functions are Store of Value and Medium of Exchange.
Where Bitcoin might have a future
If you happen to produce (be paid) more than what you consume (pay for your living expenses) on a given timeframe (let's say, this year), you probably intend to save that surplus and actually use it in the future (let's say, for next year's vacations).
Something is a Store of Value if you can convert your surplus into it with a good chance that when you want to convert it back into actual consumption it has a similar value. On a stable economy, money is a decent Store of Value which you can use by simply pilling up money under your mattress.
When the economy goes wrong in a certain way and inflation takes over, money stops being a Store of Value (let's say that prices double in a year and thus your hard-earned money with which you planned to travel all around Europe now barely covers the initial plane ticket). There you can witness people looking for alternative Stores of Value like foreign money (like US dollars) and precious metals (gold, silver).
What's interesting is that BitCoin has been in some demand from people living certain countries where the local economy seems to be going awry, giving BitCoin the practical status of Store of Value. While that's amazing, you have to keep in perspective that BitCoin only becomes such thing when the alternatives (US dollars, euros, gold, etc) are not available.
Oh, but you are wrong! Since Bitcoins are going up in price in the future they are a better Store of Value than gold, dollars, etc.
— Bitcoin fanboy
You can hear something along the lines from Bitcoin "believers". As you probably realized, our fan is wrong. A good Store of Value has to be predictable. The damn thing is named store and not investment nor bet for a reason! Something volatile is — by definition — not a good Store of Value.
Would you like to have a safe where you put some money and have (by some obscure process) a chance of it be doubled and some chance of it be halved when you open it? While I accept that some people might like the idea of playing with such artifact, you most definitely won't call it a safe when describing it to your friends.
Therefore, right now, Bitcoin is only a viable Store of Value when you are mostly f*cked up and can't find any of the myriad of better Stores of Value around you. (Which unfortunately happens and thus Bitcoin makes the world a bit better by existing).
What about later? Once Bitcoin is less volatile? Well, for Bitcoin to not be volatile is has to stop being a game you "invest" on and have actual, concrete value. Value that is expected to be more or less stable by a great deal of people.
And so we are headed towards the third function of money: Medium of Exchange. If Bitcoin can establish itself as a good way to pay for stuff, you can't deny that it will become valuable because of it.
Where Bitcoin must have a future (to succeed)
Of course our currently fine Unit of Account (i.e, your local money) which most of the time is a fine Store of Value (piling it up in matresses or saving accounts) is also a great Medium of Exchange. We use it all the time to buy stuff and get paid!
The question to ask then is: What can BitCoin do better than local money? Let's try some answers:
Avoid taxes. If you pay me in bitcoins I (today, in many parts of the world) am not required to account for it (and neither do you!). So we can be part of the "informal economy" and avoid paying VATs, income taxes, etc. While that is probably illegal in many countries, it might be a bit hard for countries to enforce whatever law prohibits it, so it might work. But take the highlevel view. Depriving governments of the ability to collect revenue is a great way to antagonize governments. It doesn't sound like a brilliantly sustainable strategy. So let's just assume that if Bitcoin becomes widespread enough to be a pain for governments/states they will find a way to tax it. It's already happening. So let's move on to other advantages over good old local money.
Electronic, (almost)instantaneous remote transfers. That's a huge one, especially across national borders. It might also be a big deal inside some countries but I have no direct experiences there — here in Chile you only need to have a bank account and you can transfer your money to other bank accounts electronically, without any cost and with instant confirmation (although with some restrictions on the amounts, but nothing that bothers you as an individual). In fact Bitcoin's delay in confirming transactions (which depending on how many confirmations you want might take hours) is a downside for us Chileans, and for any other citizen of a country with a decent banking system. But to make purchases across countries we are left to wire money transfers and credit cards, which include some fees (3% and up) for one or both parties involved. If Bitcoin can do better, it can be the Paypal of the future. But can it?
Before answering this question, let's recap our journey so far: Bitcoins are unlikely to become an Unit of Account. It will only be a decent Store of Value if its nature as Medium of Exchange ends up working well. And to have a chance to be a good Medium of Exchange, it has to beat Credit Cards and other electronic ways to transfer money around the world. So that's why we are asking what Bitcoin does better than those "old" ways.
Fees! This is one of the usual answers. But just as I don't keep a USD account on my Chilean bank for my occasional Amazon purchases and other international credit card transactions, I find unlikely that I will hold BTCs. If I want to buy stuff in BTC I'll have to exchange CLPs to BTC and the seller will exchange their BTC to their local money. That's easily a 1% fee when considering both exchange transactions. There are also some fees expected to be charged by BTC miners once they stop receiving newly minted coins as a reward (or when such reward isn't enough to cover their costs), but still, if we set the entire fee to 1.5% that's much better than the current 3%+ of credit cards.
Of course today many consumer currently don't perceive any fee as the costs are paid by sellers, but let's just assume that sellers will find a incentive for people to use BTC if BTC transactions save them money. Check!.
Fraud is another thing people mention as an advantage of BitCoin compared with current electronic payment methods, and I think they are utterly wrong. Fraud is much more dangerous with BitCoins, just in a different way. Of course the sellers, unlike the current situation, can be sure that they get their money for the goods sold — although I wonder how they will deliver digital goods: After a couple of hours once the transaction is confirmed? That would be a huge letdown for me! — But if someone hacks any party able to transfer BTC, the danger is only bound by the amount of BTC available in the hacked wallet. That includes the consumer wallets merchant wallets, exchange wallets, etc.
Just watch what is happening at many BTC exchanges on these early days. Now think what happens when targets (i.e, machines holding BTC wallets) are much more widespread.
Market participants would have to either insure themselves against such losses, or account for them. Which ends up being the same: They would have to cover such expected losses with fees which — depending on how frequent the BTC thefts happen — might or might not increase with respect to the ones we are seeing now.
So we end up with a weak case based on potentially lower fees. That's not enough.
I think that the real battle will be on convenience. Credit card companies go out of their way to make plastic more convenient that cash when both alternatives are available. Obviously, credit itself is one of such conveniences. Also you have availability, ease of use and even loyalty points. They have succeeded in many markets, even with the inherent higher costs. How is that possible?
Because costs don't matter much if you provide a greater value in return.
I'll be ready to "believe" in BitCoins as a viable Medium of Exchange once the BitCoin ecosystem figure out a way in which I will enjoy paying with BTC more than with credit card or electronic bank transfer.
It hasn't happened yet.