Several issues would seem to impact your decision.
1. COURSES. What do you want to study? Which school – Harvard or Columbia – has more of the courses you want to take? For that, you’ll have to investigate each college’s course catalog and see what’s available.
Harvard Course Catalog: https://courses.harvard.edu/index.html
Columbia Course Catalog: http://www.columbia.edu/cu/bulletin/uwb/
2. REPUTATION: While Harvard might have more name recognition than Columbia, you should NOT be choosing a college based on a name. Instead, you should be choosing a college based upon what you could learn there that you cannot study at your current college. Employers aren’t going to care if you spent a semester at Harvard or Columbia, as your degree with still be from your current college.
**3. FOUR COURSES VS FIVE COURSES. ** Taking five courses is going to be more work than four courses, but if they are five courses you absolutely love, you should be fine. Some colleges, like Yale, require students to take 5 courses during their junior and senior years, so it’s not out of the norm or possibility for a student to take 5 courses. Unfortunately, you can’t assume that one course at Harvard is more work than one course at Columbia, as it all depends on the courses you choose and the required syllabus of each course. Again, you need to do your due-diligence and investigate the course catalog at each college.
**4.HOUSING. **Harvard does NOT offer on-campus housing for visiting students, so you’ll have to find someone nearby who is looking for a roommate. Columba does offer housing, so you could avail yourself of Columbus’s housing or look for a place of your own nearby the campus. Beyond the campuses resources, a good place to look for roommates is on craigslist.
Cambridge craigslist: https://boston.craigslist.org/search/gbs/roo
New York criagslist: https://newyork.craigslist.org/search/roo
Best of luck to you!