When photographing people in motion, I prefer to have the action coming toward me, not moving away. I think it makes for a more dynamic image. Here's an example.
Another technique that I use to get people shots when they are in a group is to position myself so they are "walking through me" and I photograph them during this process. (This is helpful for tours and other situations like that.) Also, the idea of having a photographer standing there taking pictures usually causes a few reactions and smiles along the way.
Of course the trick to all of this is you being comfortable enough to position yourself front and center in the action. Generally speaking, photo subjects are fine with this. You will get reactions such as people covering their face or giving you an odd look. But it's all part of the mix. And if you're there in an official capacity, this technique is even easier.
Give this a try yourself. Try these shots from both angles, and see which one is more interesting to you.
You can share your thoughts at the TDS Facebook page, where I'll post this story for discussion.