Looks like the intention in the winter, was to push warm air down into that lower area for sure. But, trying it both ways would be good. Do you have one direction that seems better?
so from the picture that's blowing in the foyer/entrance of the split level main entrance. If you don't use it as the main entrance blowing down will probably help circulate the air better and avoid the downward draft that would be felt in the upstairs living room on the backs of people on the couches if the fan were running upward