Your hero is only as interesting as the foe s/he is battling. Any protagonist is just some ordinary shmuck until you put evil in his/her path. Then your hero is pushed into showing courage, nobility, compassion, etc.
Roger Corman hit the nail on the head when he said: “In science-fiction movies the monster should always be bigger than the leading lady.”
The antagonist needs to be a worthy opponent! S/he has to be stronger than the protagonist or you’ve got no story. A man swatting a fly is nothing anyone wants to read, unless the fly is 600 pounds and has fangs. I’m not saying all antagonists need to kill people with ray guns. Look at Mary Tyler Moore in Ordinary People. She was a strong, implacable, relentless opponent.
Your bad guy can’t simply be bad, s/he needs to always be taking action – plotting, planning, stealing, belittling, killing, lying, leaving the seat up on the toilette – as a way to show us how bad s/he is. S/he needs to be constantly making more and more clever moves, always upping the ante. Just when we think s/he’s down for good, s/he comes back with a bigger punch. If s/he is not doing this, then you don’t have much of a bad guy, which means you don’t have much of a story.
Remember that the protag and antag don’t have to be cross-town rivals. They can be husband and wife, business partners, man against nature, or patriot against his/her own country.
Just like your hero shouldn’t be 100% good, your antagonist shouldn’t be 100% bad. The Godfather was motivated by love for his family. In Schindler’s List, the commandant was being a good and loyal German carrying out his orders. If your antag is a terrorist who loves killing women and children, then make her also love Italian opera or fine wine or have impeccable manners, anything that the reader can connect with.
It is the villain’s job to push the protag into being a hero. By doing battle with a much more formidable opponent, the protag must reach inside and find inner strength or superior intelligence in order to overcome the evil one. And the more clever and evil the antag, the deeper the protag must dig to prevail.
Every good protagonist must grow, evolve into someone better (or at least different). That can’t happen without a bad guy. In Die Hard, John McClane is in a bad marriage and headed for divorce. His wife doesn’t seem to like or respect him anymore. Enter Hans Gruber. Hans give John McClane the opportunity to show his wife what he is made of, and of course, he also becomes a better person in the process. Without Hans, McClane is just another washed up cliché cop.
The bad guy should think s/he is the hero in your story. In the example above, Hans Gruber felt he was so clever and so slick in they way he mastermind the whole crime, that he was the star, he should be the one everyone admired. And why not, nobody was smart enough or had big enough balls to stop him. Yes, he’s stealing 600 million and killing hoards of people, but stealing from mega-rich-corporations to give to the poor (himself).
So once you’ve established the protag and antag, and they are doing battle, be sure to give them plenty of face to face time. They should come to know one another very well. And for the most part, the antag should have the upper hand, until the end, of course.
Keep in mind that your bad guy is the point on which your story pivots. Make him/her deliciously bad.