I haven't played enough of Dark Souls III to fully judge yet, and I haven't played Demon Souls.
But to put what I have played so far in order of favorite to least favorite, i'd say....
Dark Souls
Dark Souls III
(Bloodborne, if you want to include it)
Dark Souls II
I think the combat, setting and lore were all pretty great. It was fast-paced and fluid, had interesting weapon, level and enemy designs, and a universe inspired by Lovecraftian horror (which is a major plus for me).
Buuuut I think it fell flat in terms of replayablility, between the limited weapon selection, armor design, and awkward/repetitive PvP mechanics. It was excellent during the first run, but got stale rather quick. I haven't gone back to it, but I got my money's worth.
All just my opinion, though.