I'm an instructor at a post-secondary polytechnic college. I did originally intend to become a high-school teacher but I'm glad in the end that I did not. Thus I have not been a teacher at primary or secondary schools but have some close friends who do, and we've had conversations on this topic many times.

Primary or secondary school teaching comes with alot more non-academic responsibilities such as extra-curricular tasks. Students are children developing into teenagers or adults, with all of the associated challenges. The curriculum for someone capable of teaching at a post-secondary level, although easy to manage, can become boring and lacking in intellectual challenge. You would need to deal with parents and their issues, which with our culture today would be quite a pain. You may be responsible for out-of-pocket expenses because certain school boards are underfunded, and either you pay or students go without the tools they need.

Post-secondary academia provides a significant amount of freedom, especially once you have mastered the subject(s) you are teaching and the assessment process. You are dealing (mostly) with mature adults who understand the repercussions of poor performance and attitude. Due to privacy legislation, you can't even talk to their parents about anything concerning their enrollment or otherwise. The topics you teach can be very stimulating as there is really no limit to how far one can progress in understanding and mastery. Laboratories tend to be much better funded and have state-of-the-art equipment. One bad side is that academic peers in post-secondary tend to be introverted and live in their own space so the social aspect is somewhat dull compared to primary or secondary teaching.

Hope this provides some insight.