Ways to speed up your teching:
Establish trade routes with him for science income, pass applicable things in the UN like Scholars in residence and arts funding. Use faith to purchase great scientists and enter the rationalism tree/take science policies like workers faculties or the one that makes speis better at stealing techs.
You probably can improve your city micro and tech pathing as well.
Ways to slow down their teching:
Go to war with them, hire someone to go to war with them, embargo them, tamper with their religion if they have one,
That said, at high enough difficulties Korea and Babylon are going to be strong techers, and without a tech focused civ you will have trouble keeping up with them. It sounds like you are going for either a culture or diplo victory, since its peaceful and not science. In that case, you need to concentrate either on preparing a bunch of great scientists for bulbing to internet, or simply allow yourself to fall behind in tech. Being behind in tech is least important to a diplo strategy.