I greatly prefer the world building and level design of Dark Souls. The interconnectedness of it all, the need to traverse the world rather than warp (for the most part), the darkness and claustrophobia as you descend deeper vs. the light and openness as you approach Anor Londo. The fully-formed characters like Lautrec, Solaire, Siegmeyer, Gwyndolin. The sinister secret of Petrus. The heartbreaking legend of Artorias and Sif. Dark Souls is my favorite game of all time.
However, I just slightly prefer the combat and movement of Dark Souls 2. Stats seem to mean more, especially ADP and your equipment burden. I love dual-wielding in power stance. The expanded magic system is great fun.
Overall, Dark Souls is an A+ and Dark Souls 2 is an A-.