Is Harrison really a bad guy?

While he may not be the main antagonist in the scheme of the film. That role belongs to the Admiral for all his misdeeds during the flow of events.

Khan is still an antagonist no matter how you look at it.

Back in the 1990's, the Eugenics War occurred where it was a battle for superiority of normal humans vs these seemingly indestructible genetically modified super-humans. In the end, the super-humans lost and because of their rebellion, were sentence to float about space for the rest of their time in a cryogenic state, including their leader of the rebellion, Khan.

When the Admiral released Khan, his intention was for Khan to help ignite the Klingon war using his designs for warships like the Vengence. Meanwhile, Khan only agreed to the Admiral's demands because he knew the Admiral would kill the remaining super-humans if he didn't comply. All the meanwhile, Khan is putting his plan into place to get his comrades free and re-ignite the Eugenics Wars using this new technology of the era.

The only reason Khan complies with Kirk's demands is because he learns that his comrades will be destroyed when these missiles detonate upon impact. Which is also the only reason he saves Kirk as the warning was sent out to him long before the land party departed, alerting Khan to the fact that his old friends might be in danger.

From then on it becomes Khan using the crew of the Enterprise and make them sympathetic and curious as to the situation at hand, which is why the Admiral wanted Kirk to just fire the torpedoes and be done with it.

Khan then uses Kirk to get aboard the powerful war vessel that he helped the Federation design and once he is able to subdue everyone on board, unleashes literal hell up on the crew of the Enterprise with his intended target Earth, after getting his comrades.

Khan's character was cool, collected and methodical throughout the entire film, until he captured the new battleship built by the admiral.

Once that happen his true personality appears. He no longer needs Kirk's help to save his frozen crew. He starts by crushing the admiral's head with his bare hands, he breaks the leg of the admiral's daughter and then he transports everyone to the Enterprise to die with their crew.

I don't think there is any doubt that Khan was a dangerous enemy.

For a more definitive answer to your question I suggest you view the Original Star Trek Series, more specifically Season 1, Episode 22: "Space Seed". In this episode you will see that the "Bad Guy" isn't as much a bad guy as he is self-serving, but becomes a "Bad Guy" in the Original Star Trek 2 movie.

Clearly, the character "Harrison" (in STID) follows the same path. His "Terrorism" is explained as a retaliation for actions he thought were done by the real villain in the movie. But, that said, "Harrison's" abilities and sociopathic tendencies make him a dangerous adversary to the Enterprise crew as well as the United Federation.

Well even in this version, he was banished from earth for leading an uprising during the Eugenics war. So he was a bad guy to begin with. (well it depends on whose side you are on in a supermen vs normal us war).

Also, remember the conversation with the older Spock when he says that Harrison is the biggest adversary that the Enterprise would ever face? So he might have been OK in the movie but even in this timeline he means trouble.

I also don't really see Khan as a villain. In all cases his actions could be seen as necessary, although I will admit they are fairly ruthless. He was forced into his role by Admiral Markus and co-operated with Kirk till Kirk proved himself untrustworthy. He killed Markus most likely because he saw that as the easiest way to rid himself of his most powerful enemy and the greatest threat to his people. Turning on Kirk and the Enterprise may have seemed necessary considering that Kirk had already betrayed him and it's highly unlikely that Kirk would ever allow him and his people to go free. So from a non-federation perspective his actions are quite justified in being the only way to free himself and his kind, though they were ruthless and calculating they were still understandable