Are online course offered by American University great?

If they're an accredited university or college they may have some value. The potential employer is one of the main determiners of the merit. If they won't hire a University of Phoenix (large online University) graduate , then such undergraduate degrees have limited use.

Personally if a potential candidate applied with a degree from a noted university and curriculum that specialized in certain discipline that lines up with that job with a long time presence, how could an employer have a hard time making a choice about which to hire.

You get what you pay for most times with quality education.