The value of Bitcoin over its alternatives derives directly from removing the state from control over both monetary supply and transaction censorship. Advantages include freedom from seigniorage, foreign exchange controls, and financial surveillance. These allow the money to be transferred to any person, in any place, at any time, without need for third party permission.
These advantages represent cost reduction through the avoidance of tax. Seigniorage is directly a tax, while foreign exchange controls limit its evasion. The state itself often claims political independence as an objective in the interest of limiting this taxing power. Financial surveillance limits tax evasion more generally. While Bitcoin cannot eliminate tax, or even necessarily reduce total takings, it represents a change in the nature of taxation. In any case, for those who consider the state a social good, the option to voluntarily fund it remains.
It would be an error to assume these advantages flow from the existence of a more efficient technology than employed by other (state-controlled) monies. The technology is far less efficient, yet it helps people resist state controls. It is this resistance that provides the value.