The basic mechanic of rolling a number of dice equal to attribute+skill, and checking each die individually against a variable target difficulty in order to get a number of successes, was what was copied. The only real innovation is that they switched from d6 to d10, so you could have more variance in the target numbers without having to explode the sixes.
No credit for innovation on stat generation methods; that's the first thing that anyone can house rule trivially. Minor credit is given for using different stats and skills, but some of that is just because the setting is different. Full credit for innovation on all of the different powers and clans and whatnot, but that's not really a "rule" thing. And the damage calculations were also different, as you say.
Over all, Vampire shows all of the signs of being a Shadowrun heartbreaker, except in that it actually managed to surpass its source material in terms of popularity for a while. You could make a strong comparison to Palladium Fantasy, which was a D&D heartbreaker, but was also more popular in the nineties. That doesn't make it any less derivative. Nor do I mean to cast aspersions on World of Darkness, by any means; being derivative is not necessarily a bad thing. It's just that credit for the basic system mechanics - what people think of as "the White Wolf dice pool mechanic" - belongs solely to Shadowrun.