The sound intensity must be factored by the ear's sensitivity to the particular frequencies contained in the sound. This is the kind of information contained in equal loudness curves for the human ear. This is one of the motivations for using the decibel scale to measure sound intensity. A general 'rule of thumb' for loudness is that the power must be increased by about a factor of ten to sound twice as loud. Thus, a direct physical measurement of intensity, or even sound presssure, is almost meaningless in sensory terms unless it is referenced back to a threshold value.
Sound levels are directly meaningful in sensory terms.
The concept of acoustic power is not readily considered by most people, due in part to a preoccupation with sound pressure. To put it simply, sound pressure is the result of sound power. Sound power is the cause, sound pressure is the effect. The goal in loudspeaker design is to maximize the amount of acoustic power available from the device, given the constraints and trade-offs between the available parameters. One acoustic watt is equivalent to 107.5 dBSPL at around a meter from an omnidirectional source.