Before I note upon the worlds, I will first give a comparison of difficulty for those who don't care enough to read complete analysis. Overall, the games have very similar difficulty, but they are reversals of each other. Demon's is much harder in terms of general mobs, the main reason being the lack of poise, but also i think the moves of many enemies are more difficult to read and adjust to that in Dark. However, these more difficult mobs fail to overpower when you can have magical healing grass and regen items available left right and centre.
However Dark's bosses are more difficult on the whole. Every boss in Demon's I either killed on the first or second attempt (the exception being the maneaters, not because i found them hard but because i decided rolling off a bridge would be a good idea). If you compare bosses such as phalanx, armour spider and adjudicator to those such as the gargoyles or quelaag, there is pretty much no comparison. Later bosses even the dragon god and maiden astrea i killed on the first attempt. I think though that the reason for this is the fact many bosses have a quirk, such as fool's idol's invincibility or Old Hero's blindness, whilst Dark Soul's bosses focus more on difficulty, with less have features like this (though seath and bed of chaos break the mould).
The worlds i see are very much the inspiration for areas in dark, the prison in 3-1, all of world 1 and valley of defilement are very much carbon copied in Dark souls, and also bosses seemed to be reminiscent of one another, however the bosses seemed more innovative in Demon's souls (my personal favourites being the phalanx and fool's idol, i thought the ideas were particularly unique for those two. My personal favourite world was Latria, the atmosphere was haunting and intriguing, with 3-2 being the best area in my opinion, stepping for the first time out into the wide expanse suspended in nothingness was awesome. I also enjoyed the insta kill you receive as reward for killing the tutorial boss (even though i created a 2nd character to see what happens when someone mentioned it), I thought it would be a very good welcome to a new player introducing what it's all about lots and lots of deaths.
In terms of comparing equipment and such, the amount available was a slight disappointment, nothing compared to the variety i found in Dark Souls, I could even count the number of armour sets I found on my fingers.. However I loved the idea of using boss souls to create spells (even though i couldn't use them by self limitation) and the upgrade system i feel is much better and less restricted than in Dark Souls. Seriously where the status effect weapons gone?!
Finally I come to my personal preference between the two. It has to be Dark for me, and i don't doubt it is because that is the first one I played but i feel that the more variety with the weapons and armour and the more free world to explore wins it for me. (even though this won't be popular with Fex and Emergence I'm sure ).
Anyway, essay over. Please feel free to discuss what I've written and such. If I've missed anything particularly vital then also mention that too so I can add it it