Bitcoin tries to do too many things. One of the things that it claims to do is be a medium of exchange of value, i.e. a currency. But its really kind of fails as a currency; nearly everyone actually using it to exchange value is really just using it as a just-in-time proxy for some other currency, i.e. businesses accepting BTC nearly always actually accept whatever the BTC equivalent of a USD (or other fiat) price is at the given moment and instantly convert it back into their fiat currency of choice when the transaction is completed. This is in fact the primary service Coinbase offers (at least, for merchants).
And of course bitcoin has some flaws that make it hard to use as a currency in this fashion; as mentioned in the fanfic, it takes a decent amount of time before you can be confident that the transaction has actually gone through. Delays like that are acceptable in some transactions, but not in all.
Furthermore, this use of bitcoin as an exchange of value is also obscured by the fact that people try and use bitcoin as an investment vehicle, try to use the blockchain for other purposes (e.g. as a digital notary), etc.
All these reasons are why I too have been very skeptical of bitcoin. As far as I'm concerned, most of the "value" of bitcoin is driven by people treating it as an investment vehicle, and this leads to a lot of instability in the value. Without a long-term stable value (or predictable trend), it's hard to actually use it as a currency in its own right; anyone not using it as an investment vehicle is encouraged to hold a bitcoin position for as short a time as possible to minimize their risk.
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Stellar is a lot more focused. It's strictly acting as a medium of exchange, and in fact encourages you to not even use STR as a currency but instead to just use currency as a currency. STR will have some intrinsic value, but that value will likely be very stable, based on some particular fiat currency (I'm assuming USD but it doesn't really matter which one). It will largely just be used to facilitate exchanges between other currencies, like USD and EUR. Instead, people will trust various gateways to issue credit in the currency of their choice, and trade that credit.
Not only does this insulate all parties from any market instability (as the value of 1 USD is always 1 USD), but the whole mining infrastructure is also gone, replaced by a consensus algorithm, which means transactions happen nearly instantly. On that note, bitcoin fans probably think dropping mining is a huge mistake, but Stellar transactions are already based on trust (you have to trust the issuer of any credit you're accepting), so extending trust to the network itself seems reasonable; you trust that the stellar service provider (stellard) you're connecting to has chosen a set of other peers that will not collude, which prevents you from being defrauded.
These changes obviously mean the investment vehicle angle is gone (well, you can invest in STR, but the price is likely to be stable long-term, stellar has inflation too which encourages spending instead of hoarding), as is any of the other messing about with the block chain. All that's left is the currency angle, and Stellar's approach makes a hell of a lot more sense than bitcoin.
It remains to be seen whether Stellar will get the widespread adoption necessary to actually succeed. But I hope it does, because it looks like it might actually work. Perhaps someday banks will start acting as stellar gateways, enabling nearly-instant transfer between any two people with accounts at participating banks. Basically, Stellar seems like it could do what Dwolla has been trying to do, except without even the 25 cent fee.