Many traditional branding methods, rely on values & attributes to define brands, but these tend to be similar in competitive markets. “Innovation” and “Simplicity” come to mind as current popular values. “Empowerment” and “Enabling” were very strong about 5-6 years ago in the bubble days.
Values & attributes also tend to be limiting when things get intricate, they start to merge or contradict, broaden their meaning to the point they become useless at creating focus, or worse turn to generic clichés.
Often they will just float out there in their pure bright solitude, increasingly disconnected from your organisation, your brand, what you meant for them to do. From meaning.
Stories are closer to the way people interpret, articulate and communicate (complex) meaning in most contexts.
That’s another reason one-word-equity (whether you refer to the “new” concept or the “old” one) just can’t work – The association networks people have about brands are tangled, fluid, complex things. Trying to introduce focus using this “laser” approach is hopeless – the mind will (and should) resist. Telling a story influences perception in a much subtler way.