Core or ABS?

Do you think that ripped abs signify a strong core? It doesn't. Many people with defined abs (not all but many that I personally know) have defined abs but can barely hold the plank for more than 30 seconds, balance on one leg, or do push ups without arching their back.

However, other people can demonstrate strong core strength but may not have defined abs. 

In my personal and professional opinion, I believe it is important to build your core strength primarily, and only then after, work on the definition of your abs. It's beneficial towards long term function training, everyday lifestyle challenges, sporting activities, and self confidence. 

If you had to choose, what do you think is most important? Having defined abs or a strong core?