That was apparently the original idea, that as vampires aged, they got more powerful and uglier. The Master was the original supervamp in the Buffyverse, with superior power simply because he was so old. They scraped that idea after Season One, though.
Angelus was a badass, it’s suggested, because Liam was an asshole. Even before he was vamped, he was selfish and boorish and violent - being vamped just gave him superior strength and made him harder to kill. Remember, Angel’s the one who hints that vampires retain their human personalities, when Willow’s surprised that Vamp Willow is gay, and Darla confirms this when she tells him, “what we were informs what we become”, and that his darkness as Angelus is because of his darkness when he was human.
Spike was, at best, a fair-to-middling vampire who happened to have a kick ass vampire “family” to hang around with and egg him on. His freak luck in killing Slayers doesn’t really seem to be because he’s a better fighter or stronger vamp, but because he can get into their heads and he’s persistent. And, since William was a lovesick poet/stalker, I guess that makes sense, too. Without Darla and Drusilla, he never really made it back to Big Bad status, although he tried.
So the simplest answer, once we move past Season One, is that vampires retain at least some of their human traits, and just like some people are bigger and badder than others, so are some vampires.
The ubervamps in the final (television) season were something else again. They were Turok-Han, an earlier, more savage race of vampires, analagous to Neanderthals in human evolution. They’re stronger, physically, and can withstand staking and holy water, but they don’t appear to be all that bright, and they will still die if beheaded or subjected to sunlight.