Right - I count being the official money of the eurozone as an extrinsic quality, not an intrinsic one. Fiat money is intrinsically worthless, just like BitCoin. Unlike gold which has utility in that its market value isn't just based on its speculative value, but also what it's used for - a lot of things like electronics and jewelry that make it so that demand for gold will always be non-zero - fiat money is just paper, at the very most, and at the very least just bits being willed into existence by a central bank that may or may not later be printed into paper money.
Its officialness gives it two extrinsic qualities: 1) It can be used to pay taxes in some countries and 2) It is unlikely to be outlawed.
To me 1) is not special. In my view this just means there will always be at least one vendor that accepts the US Dollar (the US government) and while that's a nice guarantee, it makes the dollar different only in degree, but not kind, from BitCoin.
2) is slightly more interesting because it means that while Bitoin may be outlawed, the dollar will most likely never be outlawed, and the current regulatory framework governing money transfers, financial reporting, etc. is likely to stay consistent.
I believe BitCoin will be regulated more heavily, but not altogether more heavily than the dollar, but it will be not outlawed. Thus I think BitCoin in the end will not be meaningfully different from other fiat money, but it will offer things that fiat money can't offer, like unlimited electronic transfers over the Internet at small cost.
Of course, like anything I don't know the future. Here's to hoping.