I hope by core you mean more than just the rectus abdominals and external obliques that you can see in the mirror.
If you combine core and strength training you will get the best results. You can start off with a greater core and muscular endurance focus, then over the next 6-10 weeks transition into a strength focused program while continuing to make improvements in your core.
Direct core work is good, but to be really effective there should be a transition from core work to specific tasks...in the case of a strength athlete, dead lifts, squats, presses, etc. Not to mention, dead lifts and squats place a great load upon the core as well.