Both contain B vitamins, the extract simply contains them, whilst live yeast secretes them.
Both potentially alleviate inflammation in the gut. Studies have shown that yeast supernatant (the liquid left when you remove the yeast from the culture!) also reduces inflammation, whilst cell walls from S. cerevisiae (and the variant, boulardii) contain Mannose-rich Oligosaccharides (MOS). These bind to a component of pathogenic bacteria (mannose-containing lectin) and prevent it from binding to the gut wall (and thus preventing inflammation and all the nastiness that goes with it!).
So, you can feed BY or Yea-sacc, but as Oberon says, supply of extract is variable and I've switched for exactly the same reason. The studies are all very well, but somehow I don't think every brewing batch is standardised according to cytokine assay results...
Another advantage of live yeast is that it forms a protective 'biofilm' in the gut, so in theory you can feed less.