Value is based on supply and demand.
The only difference between Gold and Bitcoin is that if people stop using them for monetary exchange Bitcoin will be worth 0 and Gold will be worth something greater than 0, but that amount would still be much lower than it is today.
Another way to think of it; It is personal fiat (I think it so) that gives anything value. It is government fiat (I declare it so) and force that gives the dollar value.