Dark Souls 2 is categorically the better game, imo. Some context: I've played somewhere between 300-400 hours of Dark Souls across all three platforms. And every time I get past Anor Londo, my will to continue is sapped. I just do it and get it over with, but I don't enjoy any of those areas with the exception of the Duke's Archives. But then I hate the Crystal Caves. New Londo is alright, but it's over really quickly, and the ghosts are just annoying.
The most common complaint I see is that Dark Souls 2 doesn't have the connected world of the first. But once you know how it connects, the net effect is just that it feels really small. Dark Souls 2, by comparison, feels HUGE. And it definitely is bigger and longer than Dark Souls. The sprawl of the world, rather than the corkscrew nature of DkS1, feels like a deliberate design choice. I think the people saying the level design is worse are misguided. I mean, it's fair if you like that style of design better, but that doesn't make Dark Souls 2's design worse imo. And individually, I like all the areas better, though sometimes the bonfires really are too close together, and sometimes you get a pretty long run to the boss (Brightstone Cove), so it's slightly inconsistent. But I don't miss boss runs like going from fucking Firelink to the Four Kings if you screw up, dear lord. I know there are lore reasons for there to be no bonfires in New Londo, but come on son.
I think the complaints about the bosses are somewhat more valid, but only because there isn't really any boss that struck me as incredibly novel in Dark Souls 2, except the Executioner's Chariot. Some of them aren't great, but there are also more bosses than in Demon's and Dark Souls combined, so I'll still take it. I'd put Darklurker up there with any Dark Souls boss, though, but he's optional and easily missed.
Story-wise, although I find it a lot more confusing and vague, Dark Souls 2 blew me away with some moments, like the end of the Crypt. From Drangleic Castle onwards, the momentum is incredible and the areas are fantastic. People complaining about Shrine of Amana? Git gud. Seriously. Learn to roll. Bring a bow, or throwing knives. Don't go crying because you're pure melee and ignoring the many, many consumable items you can use to make your life easier even as pure melee, or crossbows, or shields with strong magic resist. I never felt like the game was cheap at all, there wasn't a moment like those asshole Anor Londo archers, but then I'm also a better player than I was then, so ymmv.
So yeah, better level design, more intriguing story, more bosses, more variety in builds and combat styles, I think it's absolutely better, no caveats. The only thing it suffers from is that it just isn't new, it is mostly more of the same. But better. That's all I ever wanted, though. This series has improved with every installment as far as I'm concerned.