For both sections, this issue was an emotional/psychological/political one. For both sections (though more for the North) it was also an economic issue.
Both sections were very interested in this issue because they wanted to be able to feel that their side was getting its way. They wanted to feel that the federal government worked for them. Therefore, they wanted their system to spread into the territories so that they could feel that America was a country that was solidly behind their system. In this way, they were after the intangible benefit of feeling that their side was on top.
But both sides were also interested in the issue for economic reasons. This was particularly true of the North. Both sides wanted the chance to be able to move West and find more opportunity. If the "wrong" system were set up in the territories, they would find themselves cut off from this opportunity.
In this way, there were tangible and intangible reasons for caring about this issue.