Doug Merril at A Fistful of Euros has, I think, gotten the right answer to the “soft power” issue:
Here’s a suggestion cribbed from an adaptation of an old tabletop game: power and influence. Roughly speaking, power is the ability to make people do things (or suffer the consequences); influence is the ability to get people to do things on their own (to gain the benefits). NATO has lots of power (and a good bit of influence), while the EU has an enormous amount of influence, but less power. Pointy-haired bosses use their power; good businesspeople use their influence.
Influence is not a second-rate type of power (soft rather than hard); it’s a separate, if related, capacity. So: power and influence.
I think that captures it correctly. In particular, I like that this power/influence issue doesn’t precisely track military/non-military distinctions. For example, while it’s certainly true that the EU doesn’t have as much power as (say) the United States it’s still the case that economic giants like the EU and Japan have a decent amount of power. Economic coercion is, at the end of the day, still coercion and it can be made to work in the right context.