Not better, or more powerful just different.
So in many superhero movies, especially before the genre got better, by the 3rd movie it was all about cramming in as many villains as possible. Take Spiderman 3 for example. Ugh.
But the Dark Knight franchise does it right--it's less about that and more about the unique challenges each villain brings and the themes interwoven throughout.
And there's cause and effect. You kill off the big bad? Ok, well, what happens when there's a power vacuum? What did the big bad have in place if he died? Ask questions about the original narrative--who loses that's on the fringes?
In Iron Man 2, you've got villains who aren't more powerful than the ones in Iron Man 1. They're just different. (Let's not talk about Iron Man 3, because that one wasn't as narratively strong). Iron Man 1's big bad was ultimately Stain or Warmonger, but even knowing that he was the hand behind it all was a problem. He died, but that didn't prevent Iron Man 2 from being awesome. And Iron Man 2 was about a villian that came from the actions of Tony's father, and his father's legacy.
Straight villains aren't always the way to go. Take, for example, Marvel's Civil War. Who or what is the antagonist there?
No matter what, it's got to be story, world, and character-driven. In Star Wars my main problem with the new stories was that the rebellion didn't become the government of the New Republic, but was still somehow the scrappy underdog. It would have been much more interesting to me if the remnants of the Empire had taken on the role of a terrorist organization or movement within the New Republic. EDIT I mean how many of the soldiers on the Death Star had a family? Vengeance would have been an interesting motivation,
One thing that you can do is make the villain an organization. Like Hydra. Cut off one head, yadda yadda...with the second Captain America, this is explored, and to the hero's horror, the very organization he had served (S.H.I.E.L.D.) had harbored this corruption.
Events from this movie directly tie in with Caps unwillingness to be beholden to a government. Just like events from age of Ultron shaped Tony's opposite view. The most interesting thing is that before those events it's pretty likely that Tony would not have ever agreed to restrictions like that (and he testifies before congress on those views in IronMan 2) and Cap, whose entire thing was trusting the chain of command as a soldier would have been more likely to bow to those restrictions before Winter Solider reversed those views.
Point being, that it isn't impossible to do, and there are lots of examples, especially within the Marvel franchise. While they do escalate power level for Avengers 3, in the meantime, they've told lots of different, engaging stories with the same characters that have been excellent.
Interesting and escalated aren't the same thing...
However, if you're talking about one story and killing off the big bad, and just continuing rather than making it the end of a story, that's a whole different issue...