From my experience strategic thinkers are easier to come by, especially in agency setting, but the implementation of community management is a hard-earned specific skill set acquired from deep hands-on practical experience. So my vote is clear: execution.
A Community Manager needs to have a strong grasp of strategy and broader business objectives, but the community’s success will be greatly impacted by how well it is managed, nurtured, grown and sustained. It doesn’t matter how great your strategy is if it falls over when implemented.
It should also be noted that often the business wants & needs vary from the community’s wants & needs, and it is important that the community management can tread this tightrope whilst negotiating competing interests. The strategy should be shaped (to an extent) by what’s happening on the frontline, and a great Community Manager should be able to feed this info up/out. All of which points to the value of successful execution.
To which I’ll add the term ‘execution’ is sometimes an ill-fit with the community as it implies there is some sense of completion, when it fact it’s an ever-evolving beast!