I know very little about World of Darkness except for a Vampire game I played back in 1994. Does it suppose that your character has to be a vampire? Or can you be a mortal, fighting the vampires? (Really, I am completely ignorant of this system.)
Vampire is one of many things the system can do. In the New World of Darkness, there's a core book that gives you all the rules for running a basic game of bog-standard mortal human beings, plus ghosts. Once you've got that, you can buy another book to tack on a supernatural element:
Second Sight for psychics,
Mage for modern magicians (think Dresden Files),
Vampire for vampires,
Werewolf for werewolves,
Promethean for soulless Frankensteinian abominations,
Changeling for people kidnapped by the fae,
Hunter for monster hunters.
The books may look daunting, but
Mage is the only one that really rivals D&D 3.5 for complexity. Running a game of Core +
Second Sight would be fairly simple, and it's one of those games that doesn't really require the players to know the rules perfectly to be successful. Mostly the books are full of story ideas and plot hooks, rather than endless rules text--it's one of the few game lines I really enjoy reading, even if I don't intend to run a game. It's all on a dice pool system, although much simplified from the version of Vampire you played in the 90s. Add attribute + skill - difficulty, roll that many d10s. Rolls of 8 or higher are successes, and you usually only need one success to accomplish something.
Here's a
quickstart guide to get you started. This uses Vampire for examples, since it's the most popular line, but all of the lines function on the same basis: point-based character generation, attribute+skills, etc.
Oh, and given your stance on Bennies/Flaws, I think you'll like what nWoD does with flaws. They don't get you any extra character points, but if they hinder the character in the course of play, the character gets a tiny bit of extra experience at the end of the session. It cuts down on this garbage: