This game is honestly everything you'd wish for, and more. It has punishing difficulty, more items, more exploring, more variety in areas, more and harder bosses, 'cooler' weapons, better upgrade system, less exploitable heal system than the grass system of the previous installment. That all being said, it's not a true sequel. The story and background are completely unrelated, and although the new story leads to loads of comparable game-play, it's still different. The game isn't divided into 5 areas any more, instead it's a lot more free roaming, which really deepens the game. You will not see the whole game on your play-through, and a new covenant system enables you to truly explore the game with multiple characters, multiple times, and still keep being surprised by all the new things you'd come across. The online has also been improved on. You can make it harder for enemies by invading, but you can also release a monster in another persons world, which makes the whole level they are currently in a lot harder until he defeats the 'source'. Another nice touch are dropped items which wander through online games, and become more powerful as they are not found from game to game (only up till a certain point of-course). It has invading again, but also good old regular 'phantoms' that can help you out. This game is truly a must buy for any Demon's Souls fan.
Review for everyone else:
I hope you just happened to miss Demon's Souls. Else you might just have missed one of the best games that has come out on the PS3, perhaps even this gaming generation. But it doesn't matter. Dark Souls as it's predecessor is an action-rpg, in the true-est sense of the word. There is a really tight control on your character, the game-play consists of timing attacks, choosing strategies, blocking at proper time, and a lot of dodging enemy attacks. The game has a leveling system, which is really a necessity in a proper RPG. This game does this really well. Enemies give 'souls' normally basing on how difficult they are to beat. You use these souls to level up at certain spots in the game. This is where the difficulty starts at though; if you die, you might lose hard earned not spend souls. You get one chance, starting back at a bonfire ('checkpoint') which is often quite a while back, and you'll have to fight your way through all re-spawned monsters again, till you reach the spot where you died, at which you can pick up your souls if you haven't died in the mean while. If you did die, those souls are lost forever. This game works with quick-saves, and you'll have to endure every big mistake you make. Don't let this all be offsetting though, because once you are properly in the game, you'll notice wanting to play more, thinking of new strategies to counter certain enemies, attempting a same level again and again, each time coming further. After a while you'll notice how relatively easy some parts became compared to how hard you think they used to be, and perhaps you'll even start seeking out new challenges. This game truly has huge immersion, which before you'll know it, makes you beg to play it more.
Dark Souls could well be what you've needed in your gaming life. Most games these days lack challenge, but you'll find a rewarding difficulty in this game.