Jesper doesn't give a shit about anything when we first see him. He just wants to be a lazy slacker NEET. Kuzco's got more ambition in life, and more of an ability to casually commit cruelty towards others. He was willing to kick people out of their homes and destroy their village in the movie; I don't feel like Jesper would be okay with that kind of thing.
They're both privileged and arrogant, but Kuzco was spoiled due to his status, and it encouraged his worst qualities. Meanwhile, Jesper's father appears to be trying to coax his son to be less of an entitled, sheltered shit. Kuzco needed to tone down his selfish egoism, while Jesper needed to try harder to do something with his life.
In the beginning of the movie, Klaus is a bitter stoic loner who doesn't want to hang out with other people or talk to them. He's struggling with grief and he's shut himself off from the community.
Pacha is a mellow family man who's happy with his life. He socializes with other people in a normal fashion, and he's basically just an ordinary guy. Also, he gets into some really wacky events during the movie and takes part in lots of comedic scenes. Klaus is too grim and serious for that kind of thing.
Jesper/Kuzco have a bit more in common, but Klaus/Pacha are very different.
The dynamics are different as well. Kuzco and Pacha have conflicting agendas which cause some hostilities between them. Jesper was initially scared of Klaus while Klaus was too anti-social to like his idea at first, but other than that, their team-up has a lot more mutual co-operation.