“Your core is weak” This statement is one of the biggest truths and misconceptions associated with low back pain. I have never met anyone with “to strong” of a core. Your core can always be better and different tasks require different core demands. A rotational athlete needs to be strong with rotation and anti-rotational, most athletes need mid-line core stability, with can be very different than core strength. Whatever your choice of activity you should have a core routine that you keep consistent with.
There are many other sport specific core exercises and most depend on core stability. It is very hard to build core strength without stability first. Choose the best level for you and your sport.