There's enough space for both world-scale and local-scale, and a large enough cross-over audience interested in both, as well as specialists in areas of each. As you've identified in your question, we've had good world-scale questions with good answers; and good local-scale questions with good answers.
I've seen no evidence that on is displacing or drowning out the other: the site is still very young, and so site activity is still in the early days of growing, so new questions stay on the front page for a day or more. And that means that anyone passing by the front page, will find both local- and world- scale questions on a wide range of topics. That's our main shop window for now, until we build up a big body of awesome content on the search engines.
The launch process for this site is that we are trying to build up a body of content, and a group of regular contributors, as well as lots of interested passers-by.
The targets we need to hit to get this site out of beta, and to fully launched, are:
- over 15 questions per day: currently 1.4
- over 90% answered: currently 96%
- over 150 users with 200 rep: currently 57
- over 2.5 answers per question: currently 1.8
- over 1500 visits per day: currently 113.
As you can see, we've got a lot of work to do; in particular, in building up the number of questions per day, and the number of visits per day. For now, that probably means keeping the audience, and the scope, sufficiently broad; while keeping the topic sufficiently well-defined enough to create a group of regular users with expertise in a topic that doesn't get too sprawling or unwieldy.
You can follow these stats on the relevant meta question.