You should play Demon's Souls first before you leap into Dark Souls so you can notice the changes.Not to mention Demon's Souls worlds taking everything into consideration is better as a whole than Dark Souls imo.Not that Dark Souls is bad it just has really low areas that seems rushed.
I'd play Demon's Souls first as well.
I can't agree with this post's point that the "worlds" are better. Dark Souls had much more ambitious levels in terms of interconnectivity. Demon's Souls really is just levels.
Though I think Demon's Souls had a much more oppressive atmosphere. Dark Souls was more melencholy. Not that one is better than the other, but it is what it is.