The first game is definitely better in story and lore, but Dark Souls 2 has far better mechanics (both in the mechanics themselves and how things are balanced). Pretty much every weapon is viable in PvP. Covenants are more streamlined (like there are no fluff ones like the Princess Guard or anything), though there are a couple of questionable design choices (there is no full red eye orb anymore, only cracked ones and the only way to restock is to fight in the new Darkwraith arena, Brotherhood of Blood now, and win matches).
Soul memory isn't great, but there's a ring that prevents you from gaining souls which allows you to stay in the soul memory bracket of your choice.
Overall, it's a really great game. The only thing it's missing is Dark Souls 1's atmosphere, which it sadly lacks in most places. The DLC is more fun than anything in either games, though, with the atmosphere to match (in my opinion).