Hm...personally, I had a lot more fun with Dark Souls II. The game felt more friendly to new players, and because of it, I was able to go back and enjoy Dark Souls, whereas before, I hated that game. I couldn't figure out how to play, and every time I asked for help, I got mocked.
All that being said, I think Dark Souls is probably the better in terms of story and lore. It's all connected, it builds the world and, if you have a bit of imagination, you can come up with your own stories that are totally possible for why things are the way they are. The level design is also much better, as there is nothing quite like that feeling of finally unlocking a shortcut after barely managing to drag your half-dead corpse there.
Dark Souls II's lore kind of fails in that regard. The DLCs fix some of it, and the new item descriptions certainly help too, but this one feels like they were being mysterious for the sake of mysterious. Example: why is there a bell tower in The Lost Sinner's area, when there is no other connection to the Old Iron King? I have my own theory, but there is barely any evidence. And what, exactly, is that cat? And for the longest time, we had no idea exactly what it was that a certain character did to anger an entire race (fixed with the update, finally, but man...)
A lot of the game feels like the characters and developers going, "We know what's going on, wink-wink, nudge-nudge...but we're not going to tell you."
If you're forced to choose, and you value atmosphere, story, and just a sense of awe and exploration, then I think Dark Souls is probably the better choice. However, that doesn't mean you should just give up on Dark Souls II. Do try to play both if you can.