Combat is the same, but you might find it slightly faster. Backstabbing is a little harder (until you get used to it), and parrying is easier (at least, I found it easier)
Dark souls fan here. I've just got Demon's souls after finishing my fourth run through of it's sequel. Any advice for someone who has never played Demon's before?
Dan has touched on the tendency. Personally, I'd encourage reading the wiki about tendency against Dan's advice () just to get your head around it.
Weapon scaling is more effective in demon's than in dark.
You don't need to worry about upgrading armour as you can't - just focus on weapons and shields etc
Whenever you kill a boss, you'll get your body back. Soon as this happens, go back to the nexus and kill yourself to put yourself back in soul form. (As Dan says, it's very detrimental to tendency, if you die out in the field in body form)
Magic is very effective against most bosses.
Once you've opened up the first level (1-1), you don't have to do 1-2 straight after. You can go to any other of the worlds first areas (2-1, 3-1, 4-1, 5-1 etc) Doing this means you can explore wherever you like to get items you want in the order you want (Once you've decided what you like that is!)
When you kill a boss, you normally get their specific soul, ala Dark souls. As in Dark Souls, don't consume these until you've unlocked a particular blacksmith that can "ascend" items with the souls.
Watch out for knights with red eyes, and black skeletons